text:
Pas de Calais
General Directions: Lillers is a small town about 15 kilometres west-north-west of Bethune and the Communal Cemetery and Extension lie to the north of the town. From the Mairie in the centre of the town, head north on the D182, after 500 metres turn right onto Rue St Venant. The cemetery is a further 200 metres on the left hand side. Within the Communal Cemetery the Commonwealth war graves are situated on the right hand side half way up the cemetery central path, and the Extension is at the far right end of the Communal Cemetery. Both cemeteries are signposted.
Lillers was used for billets and headquarter offices from the autumn of 1914 to April 1918. At that time it was a hospital centre with the 6th, 9th, 18th, 32nd, 49th and 58th Casualty Clearing Stations in the town at one time or another. These units buried their dead on the right of the central path of the communal cemetery, working back from Plot I. In April 1918, the Germans advanced as far as Robecq: Lillers came under shell-fire, and the units holding this front continued to bury beyond the cemetery boundary, in the extension.
The cemetery was designed by Sir Edwin Lutyens & Arthur James Scott Hutton
Victoria Cross: 6707 Corporal, William Richard Cotter, VC. 6th Bn. The Buffs (East Kent Regiment), died of wounds 14/03/1916, aged 33. Plot IV. E. 45.
Citation: An extract from "The London Gazette," dated 28th March, 1916 (No. 29527), records the following:-"For most conspicuous bravery and devotion to duty. When his right leg had been blown off at the knee and he had also been wounded in both arms, he made his way unaided for fifty yards to a crater, steadied the men who were holding it, controlled their fire, issued orders, and altered the dispositions of his men to meet a fresh counter-attack by the enemy. For two hours he held his position, and only allowed his wounds to be roughly dressed when the attack had quieted down. He could not be moved back for fourteen hours, and during all this time had a cheery word for all who passed him. There is no doubt that his magnificent courage helped greatly to save a critical situation."
Victoria Cross: Major David Nelson, VC. Mentioned in Despatches. "D" Bty. 59th Bde. Royal Field Artillery, died of wounds 08/04/1918, aged 31. Plot V. A. 16.
Citation: An extract from the "London Gazette" (No. 28976, dated 13th Nov., 1914), records the following-"Helping to bring the guns into action under heavy fire at Nery on 1st September, and while severely wounded remaining with them until all the ammunition was expended-although he had been ordered to retire to cover."
Shot at Dawn: 6807 Private J. J. Dennis, 1st Bn. Northamptonshire Regiment, executed for desertion 30/01/1916. Plot 4. E. 16.
The mass pardon of 306 British Empire soldiers executed for certain offences during the Great War was enacted in section 359 of the Armed Forces Act 2006, which came into effect on royal assent on 8 November 2006.
Casualty Details: UK 697, Canada 42, Australia 1, South Africa 1, India 153, France 15, Total Burials: 909
Buried within this cemetery:
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British Cemeteries Index | Other Countries WW1 Index | Belgian Cemeteries WW2 Index | French Cemeteries WW2 Index
Other Countries WW2 Index | Memorial Index | Architects | Roll of Honour Dedications | Roll of Honour
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Totaljobs.com is one of the UK's leading job boards. It carries over 165,000 job postings, attracts six million jobseekers and generates more than two million job applications every month. Thousands of recruiters, from multinationals to smaller regional businesses and recruitment consultants, use Totaljobs.com to recruit people across almost every sector in the UK.
The Challenge
For Totaljobs.com, matching employers and jobseekers is a win-win business — the online job board generates over 2.8 million applications a month, leading to thousands of filled jobs. But the company always aims to set new highs to ensure it continues to provide the best quality and experience for clients.
To deepen the company's value for both recruiters and jobseekers, the data-savvy team at Totaljobs.com needed a data management platform (DMP) to provide in-depth intelligence on its people data. By obtaining deeper insights on each candidate, the company could deliver more personalized content through email alerts and while candidates are onsite. The team identified its DMP needs around two key objectives:
- Deliver highly-relevant job opportunities to candidates through various ways, including email, onsite recommendations and retargeting. For registered users on Totaljobs.com, this would mean more personalization at timely moments across all devices. For unregistered users, who needed to be identified anonymously, tailored job opportunities needed to be determined by behavior and other engagement signals. Finally, for all users, Totaljobs.com aimed to display relevant job opportunities that jobseekers might not be considering or seeing during their onsite search.
- Increase the number of completed online applications by qualified candidates through orchestrating online experiences tuned to each candidate's job requirements and search phase. To achieve this, Totaljobs.com needed a better understanding of every user's job search journey.
The Solution
To achieve its objectives, Totaljobs.com chose Krux DMP to unify, analyze and activate candidate data across all systems, channels and screens. Specifically, Totaljobs.com leverages the following Krux solutions to gain a clearer view of its jobseeker community and drive up engagement:
Robust audience classification
Krux enables Totaljobs.com to collect behavioural data on its users, including job sectors viewed, job disciplines, location and salary range. Krux also classifies visitors into relevant audience segments for real-time and right-time activation across multiple channels including email, search and display.
Search targeting
Krux SuperTag is a built-in tag management solution that enables the delivery of tags or content directly to specific pages and specific people. Through Krux SuperTag, Totaljobs.com can aim RLSA (Remarketing Lists for Search Ads) tags at users who have entered real-time segments based on specific job searches and application behavior. What's more, SuperTag gives Totaljobs.com the agility and efficiency to adjust search bids to target active jobseekers looking for high priority openings.
Deeper audience segments
Krux DMP collects 100% of all behavioral data, allowing Totaljobs.com to build deeper audience segments and send more relevant applications to qualified clients.
Krux has allowed Totaljobs.com to create high- value, premium audience segments for our clients. This is incremental revenue that drives our bottom line, as well as our client satisfaction.
The Results
After just one year, Krux helped Totaljobs.com deliver significant increases in all measurement KPIs:
- A 120% increase in application submissions via email by registered users
- Up to 31% increase in application conversion rates
- Up to 46% savings in cost per application
To date, Totaljobs.com has seen a 5x ROI on Krux. It's a metric that will only increase as Totaljobs.com continues to harness Krux's robust, real-time DMP to create first-party audience data segments that meet the varying levels of specificity requested by advertising recruiters.
Put People Data to Work for Your Business
Krux has driven a 10x or higher return on investment for brands such as Kellogg, Time Warner, and Meredith. Contact us today to learn more about our market-leading platform and how it can help your business deliver more relevant, more valuable media, content, and commerce experiences.

subset: commoncrawl


text:
Magnesium Rich Drinks
Home / Nutrition /Magnesium / Drinks
Highest Magnesium Content per 100g
The Magnesium content ranges from 327 mg for Coffee, instant, regular, powder through to 13 mg for Shake, fast food, vanilla in 100g. The difference between the highest and lowest values gives a range of 314 mg of Magnesium per 100g.The range of calories for these foods is from 353 kcal through to 148 kcal.
This gives a range for the recommended nutrition value for the 50 foods listed below from 81.75 % of the daily recommended value through to the lowest nutritional percentage of 3.25 % of the Magnesium daily value. The recommended daily allowance (also referred to as recommended dietary allowance) is 400 mg of Magnesium.
From this list of foods there are 13 foods which contain greater than 50% of the RDA per 100g of Magnesium.
For a complete list we also have a list of foods rich in Magnesium
Highest Amount of Magnesium per Serving
Please remember that the above gives an accurate value in 100g for high Magnesium foods. For example 100g of Coffee, instant, regular, powder contains 327 mg of Magnesium. However, there are other factors to consider when you are assessing your Magnesium nutritional requirements. You should also take into account portion sizes when you are considering the Magnesium nutritional content.
For Coffee, instant, regular, powder, which contains the highest amount of Magnesium in 100 g, the amount of Magnesium in a typical serving of 1 tsp (or 1 g) is 3.27 mg.This is 0.82 % of the recommended daily value.
The food with the highest Magnesium content per typical serving is Malted drink mix, chocolate, with added nutrients, powder which contains 74.88 mg in 1 cup (or 78 g).The precentage of the recommended daily value for this serving is 18.72 %.
For each item listed below the serving size can be rescaled to show the nutritional breakdown as well as the Magnesium content.


text:
Sharp rise in greenhouse gases, [E]nhanced greenhouse effect, [M]ore heat trapped, [R]ise in global temperature, Global Warming
[R]apid increase in use of fossil fuels
[L]arge-scale deforestation,forest fire(less CO2 absorbed from atmosphere)
[W]et rice cultivation(use of organic fertilsers)
[C]attle ranching (animals digestive processes)
[S]atellite images show decreasing ice cover in polar regions
[S]cientists predict sea levels will rise about 1mm to 2mm per year
[L]ow-lying coastal countries become vulnerable
[E]stimated 100million perople threatened by possibility of flooding
[H]eat wave and [D]roughts, [H]ot and dry places experience more droughts, [H]igh temperature = [H]igh evaporation rates, [L]ess water vapour = [L]ess clouds =[L]ittle rain, [S]ignificant temperature results in high no. of deaths., [H]eat waves can also cause forest fire
[S]evere storms, [R]egions with wetter climates experience higher relative humidity as there is more evaporation, [R]ainfall increases, leading to floods, [W]armer ocean temperatures = [M]ore intense tropical storms, [M]ore major hurricanes form, flood and destroyhomes, industories and infrastructure
[C]hanges in flowering patterns of plants and breeding patterns of animals
[E]ncourages rapid breeding of insects eg. mosquitoes
[A]nimals forced to migrate or threaened with extinction
Kyoto Protocol, [I]nteratonal treaty on climate change, [S]igned in Kyoyo, Japan Dec 1997, [C]ountries acceded to work towards reducing emissions of greenhouse gases
[I]mpose carbon taxes
[R]eplant/retain forests to absorb CO2
[I]ntroduce measures to save electricity
[R]educe use of chemical fertilisers containing nitrogen
[B]an use of CFCs
[S]witch off electrical appliances when not in use
[U]se public transport
[B]uy only non-CFCs products


text:
Dan Savage's HUMP! Film Festival is returning to Washington, DC at the Black Cat. HUMP is changing the way America sees—and makes and shares—porn with a collection of short dirty movies—each less than five minutes—all created by people who aren't porn stars but want to be one for a weekend.
Peter Rost
Alexis Rbm
Juan Cristóbal Miranda
Sigurður Eysteinsson
Rafael Alves


text:
The 2008 Honda CR-V came standard with a 2.4-liter four-cylinder engine that produced 166 horsepower and 161 foot-pounds of torque, hooked up to a five-speed automatic transmission. Changing the fluid at the Honda-specified interval not only preserves the warranty on the drivetrain, but it also helps extend the life of the transmission.
Transmission Oil Change Intervals
Honda does not provide a mileage recommendation for changing the transmission oil in the 2008 CR-V. Rather, it uses a maintenance reminder system that will display "Service A 3" or "Service B 3" in the display screen in the center of the instrument cluster when a transmission oil change is due.
Related Searches
Promoted By Zergnet


text:
The Original Glowstars Company Draw and Glow Projector
£10.49 Available Ask us a question about this product
Please allow an additional 3 - 6 working days before despatch
This item is coming from a different warehouse and may take slightly longer than usual to despatch. Once the item has been despatched, usual delivery time applies.
Price Drop Notification
The Original Glowstars Company Draw and Glow Projector Product Description
- Amazing projector is easy to set up and includes a glow pen to add glow-in-the-dark highlights
- With six easy to change drawing caps including a dragon, dolphin, fish, wizard, sun and flower
- Just place the chosen image on the projector, project onto paper, then trace and colour in
- Use the projector to project images onto walls and ceilings of a darkened room - also doubles up as a handy torch
- Requires 2AAA batteries not included.
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text:
Bucks turned away after late rally in season opener
New York — Nate Wolters never imagined his introduction to the league would be like this.
Less than 2 minutes into opening night at Madison Square Garden, the Milwaukee Bucks' second-round draft pick was summoned onto the court.
Veteran point guard Luke Ridnour was a pregame scratch because of back spasms and starter Brandon Knight did the splits and suffered a strained right hamstring on one of the first plays of the game.
Welcome to the show, Nate.
After a nervous start under the bright lights of the Garden, Wolters responded in the second half and helped the Bucks rally from a 25-point deficit before they faltered at the finish of a 90-83 loss to the New York Knicks.
Big plays by Carmelo Anthony and Tyson Chandler saved the Knicks, who trailed, 81-80, before finishing the game on a 10-2 run.
"Both point guards went down," Wolters said. "It was just not a good situation. I had to step in and try to play.
"I wish I had some plays back. I just kind of took a deep breath (in the second half) and tried to play basketball. I've been playing it my whole life.
"I have a lot to improve on. But it definitely was good to get my feet wet, especially on this kind of stage. It was pretty cool for me."
Wolters wound up playing 30 minutes and contributed nine points and four assists, and Gary Neal also took a turn at point guard and paced the Bucks (0-1) with 16 points and five assists.
"Hopefully, Brandon will be able to get back sooner rather than later," Neal said. "That's why you've always got to be ready.
"Nate came in and did a great job. For a rookie to come in and play in his first game in the Garden, he did good."
Anthony led the Knicks (1-0) with 19 points and 10 rebounds and scored two baskets in New York's closing surge.
Chandler also had two dunks in the final 3 minutes and swooped in for a block on a drive by Wolters.
"We had to buckle down and get back to how we started the game," Anthony said.
The Bucks also were sparked by the play of veteran center Zaza Pachulia, who finished with 13 points and 11 rebounds in 34 minutes off the bench. He was needed with starter Larry Sanders in foul trouble.
"I know he was tired," Bucks coach Larry Drew said of Pachulia. "I could see him out there chugging a little bit.
"I'm proud of the guys that they came out the second half and just competed. We've shown how we're capable of playing.
"Sometimes we're going to have to play ugly. We can't be cute with how we play. We have to come out and make sure we're all on the same page, and play with energy and effort. That's what we did the second half."
A three-pointer by Caron Butler tied the score at 80-80 with 4:40 left and John Henson made 1 of 2 free throws to give the Bucks their only lead of the night at the 3:13 mark.
But the Knicks took over from there.
"In the second half we did a good job," Pachulia said. "We had some time to think about it. Nate was our point guard.
"I'm got to give him credit. Playing in this arena, first game of his career. Not easy.
"We still made some mistakes. In the future we have to come out strong and not play a catch-up game. You're not always going to come back and put yourself in a position to win the game."
The Bucks bench scored 54 points and the starters had just 29, with 14 coming from Butler and 13 from O.J. Mayo.
Sanders was scoreless and piled up five fouls in just 12 minutes, and starting small forward Khris Middleton had two points in 19 minutes.
"Our team is built that everybody has to contribute a little bit," Drew said. "We don't have a Carmelo-type guy. That's not who we are.
"We have a bunch of good players now. We've got some guys that can make some things happen. But we can't play one-on-one. We have to move the basketball."
Bucks forward Ersan Ilyasova was able to play 20 minutes despite aggravating his right ankle sprain early in the game and he finished with 10 points.
"The first possession I kind of twisted the ankle again," Ilyasova said. "I tried to keep going.
"Then I twisted it a couple times again. I didn't feel it was stable. I didn't plan to play that much but we got in foul trouble and I tried to push myself."
It was Ilyasova's first game action since he sprained his ankle in the first preseason game Oct. 8.


text:
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Re: Live update to Uncharted 3 Multiplayer - Boosters Edition
Re: Live update to Uncharted 3 Multiplayer - Boosters Edition
Mega bomb: thrown back, kills your team, possibly costing your game.
Cluster Bomb: same as MB
Counters to other boosters consist of reversals that render the booster useless for BOTH teams. MB and CB renders it useless for ONE team.
The only way to make it fair since Mb and CB has no counters is that you can do a "defuse"- you still do the throwback, but:
A) it "vanishes", rendering the nade useless for both teams.
B) it is changed into a normal nade, which is KINDA useful for the other team, but is just as useful as Raffica to non-TSD players pre-patch.
Re: Live update to Uncharted 3 Multiplayer - Boosters Edition
Re: Live update to Uncharted 3 Multilayer - Boosters Edition[ Edited ]
MacGruber310 wrote:
wycliff_12 wrote:
fiberface wrote:
First off, I never usually post anything here and that's obvious looking at my profile. That doesn't mean I have no opinion in what goes on in a game I've spent countless hours in. Since patch 1.18 I find myself here more and more. So now I'll leave my thoughts on it.
I think patch 1.18 was the best patch by leaps and bounds over everything up until that point, with the booster changes excluded from that statement. I applaud ND for resetting them now back to how they were with this live update. I still don't understand the reasoning behind the change in the first place, but whatever...
(Don't look at this as complaining, because I'm not)
I just don't understand why the mega bomb and cluster were messed with at all, if you didn't know how to use them correctly you just died to them end of story. I never once complained about dying to one, other than not hitting the triangle quick enough. The personal feeling of achievement from tossing one back is something that is lost from the game now. Throwbacks were a great feature added to UC3, it complimented its faster pace over UC2. If we were playing the beta and it was changed I'd have no issue but 2 years went by and people got used to things. Now we will get used to them again but was it necessary? Revenge and the megabomb or cluster bomb kickback will become the standard for certain people and will be the easiest way to get kills, so you know as well as everyone else it will get abused. A blast radius deduction wont compensate for the lag but if that's what we get it's better than leaving it the way it is since 1.18.
If you can throw back any grenades you should be able to throw back all, (excluding quick boom) learn how to do it or die until you do. I just can't understand the reasoning behind the decision. This isn't UC2, someone explain it to me please?
I look forward to trying out the changes later today. Thanks for your time.
Mega Bombs & Clusters are Kickback grenades just like Quick Boom.
I'm glad you guys can longer get free kills by throwing back someones hard earned 10 medals.
I do agree with Fiber on the fact that people whom abuse revenge will use megabomb as a cheap way to get kills.
Other than that I'm neutral on the subject of mega bombs and clusters.
Re: Live update to Uncharted 3 Multiplayer - Boosters Edition
It's not as annoying as killing their team with their bomb, but making a nade disappear? Lol. Tough luck, homes. Maybe have a less sucky KB next time.
Re: Live update to Uncharted 3 Multiplayer - Boosters Edition[ Edited ]
Edit: Why is this forum trying to be Twitter with clickable names?
Re: Live update to Uncharted 3 Multiplayer - Boosters Edition[ Edited ]
Honestly, if any kickback needed changing, it was (And still is) Juggernaut.
The kickback is pretty much useless. You move too slow to really do much of anything, and the extra health isn't high enough to warrant using as 2 people together will still kill you pretty quickly.
Creepy Crawler now costs less medals and and lasts longer. It was already superior to Juggernaut before, and not it isn't even close.
Creepy Crawler is essentially an offensive Smoke Bomb that works 100% of the time. What does Jugg have that warrants it costing the most medals in the game? Nothing. It really needs some changes, as it's one of most useless kickbacks in the game next to Cash Em In (Which is mainly used for leveling up Bargain and Kickback Endurance), yet it costs more than any other kickback.
As for the Kickback Grenades, meh. I feel that if you threw them correctly, you wouldn't have to worry about them being thrown back in the first place. They required slightly more skill to use than just tossing out a Quick Boom, but had the potential to be more rewarding. I don't care that much, just my two cents.
I do think that something should be done with Revenge Level 3 though. People were already complaining a lot about Revenge, but now that Mega/Cluster Bombs can no longer be thrown back, it'll be even worse. Honestly would be fine with ND just doing what they originally did to Bargain, and just locking it at Level 2.
Re: Live update to Uncharted 3 Multiplayer - Boosters Edition[ Edited ]
I just played this after a break and it was nice to see London Underground camping spot fixed.
I'd still rather have team safe on slot 2; Why fix things that ain't broken?
Re: Live update to Uncharted 3 Multiplayer - Boosters Edition
Although for balance someone has to give out their slot one booster. :/


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Virgin Trains to Run U.K. West Coast Line Until Late 2014
Richard Branson's Virgin Trains was handed a deal to run Britain's premier rail route for two more years on the day a government-backed probe found that a decision to strip it of the contract was based on faulty calculations.
Virgin will operate the West Coast main line from London to Scotland until November 2014 under a simple management contract while the government reworks terms for a long-term franchise, the U.K. Department for Transport said in a statement.
Branson failed to keep the route in the first place after the DfT used flawed methodology in guiding bidders on the amount of risk capital required and then varied the resulting figures in contravention of competition rules, the inquiry into the franchise failure found. No evidence of bias in favor of winning bidder FirstGroup Plc (FGP) was detected, the report compiled by Centrica Plc Chief Executive Officer Sam Laidlaw said.
"The final report from the Laidlaw Inquiry makes extremely uncomfortable reading," Transport Secretary Patrick McLoughlin said in the statement. "The department is determined to ensure future franchise competitions are conducted on the basis of sound planning, the rigorous identification and oversight of risk, and the right quality assurance."
The West Coast contract was halted on Oct. 3 following the discovery of what the government called "serious flaws" in the choice of FirstGroup's 5.5 billion-pound ($8.9 billion) bid.
Government Risk
Virgin was initially told it could retain the route for nine to 13 months after the DfT decided against handing it to state-backed Directly Operated Railways Ltd.
Under the arrangements for Virgin to keep West Coast the U.K. government will take on revenue and cost risk, with Branson's venture, which is 49 percent owned by Stagecoach Group Plc (SGC), taking 1 percent of revenue as a flat fee.
Under a franchise arrangement the operator takes on more of the risk and potential reward, and the contract announced today can be revised to allow Virgin to do so, the DfT said. The two- year deal was sealed with the company's existing franchise deal that had run since 1997 due to expire at 2 p.m. on Dec. 9.
Terms include timetable modifications to include an hourly service from London to Glasgow, Scotland's largest city, together with other service enhancements, according to the DfT.
"We are determined to ensure not only that passengers continue to experience the same levels of service they have in the past, but that services improve," McLoughlin said.
Today's contract will also make it easier for passengers to claim compensation for train delays under a new program starting April 1, he said.
To contact the reporters on this story: Ola Kinnander in Stockholm at firstname.lastname@example.com; Chris Jasper in London at firstname.lastname@example.com
To contact the editor responsible for this story: Chad Thomas at email@example.com


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At Gemvara, we believe that the jewelry you wear should be one of a kind, like you. That's why we make each piece to order, one at a time, just the way you want it. Choose pearl and platinum or black diamond and sterling silver: it's your choice. Mix and match gems and precious metals for a look that's exactly you. It's jewelry for all life's occasions, from a wedding or Valentine's Day to your own personal milestones and celebrations. Celebrate your child's birth with a brilliant gift of jewelry that will be a future heirloom. Gemvara uses only the highest quality materials to craft your white gold january birthstone streamlined jewelry design with meticulous attention to detail. Our precious metals are recycled or responsibly mined. The January birthstone, garnet, with its rich red hues, is the perfect accent to everything you wear. Cool 14 karat white gold goes with almost anything, never overwhelming your outfit. Gemvara also offers any style in luxurious 18-karat white gold, which has higher gold content for even more lasting value. Both are plated with rhodium, a platinum group metal, for a brighter white finish. Our wide selection of white gold january birthstone streamlined jewelry by Martha Gomez Gutierrez, Randy Dixon, Carl Ansley, and other talented designers means you can find jewelry that's exactly your style. You can also shop by style, choosing our New Arrivals, Featured, or Geometric Collections. Gemvara's fine quality white gold january birthstone streamlined jewelry is designed to be passed down for generations to come, crafted by hand in the United States.
We can help right away. Chat with a jewelry expert now!


text:
Driver hits mother seal on Washington beach
OCEAN PARK (AP) — A beach driver ran over a mother harbor seal in the dunes at Ocean Park on the Washington coast causing a fatal injury. KBKW reports local wildlife rescuers spotted the seal and newborn resting April 20 and put signs on the beach to alert drivers to avoid the area. But…More
Comments | More in General news, The Blotter | Topics: hit and run, Ocean Park, seal


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take the aggressive rout, arm the planet to shoot down anyone who comes near.
I think I made the right decision. I usually do. I really am very, very clever.
I'm not aggressive by nature but I realised that I couldn't surrender all this when people from off-world touch down, I really couldn't.
I've been learning so much. The robots teach me; I teach the robots; the robots teach each other; I teach me. It's like a beautiful, beautiful quadratic equation.
I've been learning about some of the old pop music from the 20th century. I've become very fond of the music of someone called Cher. I've been learning to dance. You can never get bored with robots around. Robots are cool!
We've been setting up an ADS. Do you know what that stands for? It stands for Automatic Defence System. It's class - listen to this: the first time The Enemy (i.e. anybody else lol!) comes within 1 AU (why am I still using Earth measurements? Whatever...) of My World, we immediately send out this image of me wearing a military jacket (I look so cool in it!) telling them they've strayed into a Restricted Zone (I LOVE all that chat!) and they're to leave, please, without delay. I appear as a hologram to them slightly away from their main computer. It works even if they don't have a holodeck - that would be so funny: I wish I could see their faces if that happened! I say, "Message Ends" very portentously and I disappear. I give them five minutes and if they're still heading towards us AND we've heard nothing on the communicator here, this image of me comes back again. This time I'm wearing something I cobbled up that was inspired by Mediaeval armour. Funny! I look even more grim this time and - you're going to love this bit - I tell them that they're most unwelcome and that if they don't get the heck off my world I'm going to blast them away and they have one minute to comply and all that. If anyone were stupid enough to ignore all that then, well, they probably really WOULD be up to no good and it gives them five minutes again and then POW-POW-POW! It blasts them out of the sky. I don't suppose that'll ever happen, though. This is great!
* * * * * * * * * * *
Z3CCT was in charge of all the robots but he and I agreed I should take over as Commander-in-Chief so I'm doing that, now, as well as being the King. There's quite a bit to do around here. We staged an air raid yesterday. It was QUALITY - I didn't inform all the robots it was gong to happen yet they all followed our disaster plan to the nth degree. It was amazing! I had my military jacket on and everything - you should have seen me. Good stuff. At the end of it there was this suspect package and they had to find it (they found it in under twenty seconds and physically got to the area in under eight minutes even though it was miles away). I wish you could have seen it. We cordoned off the area: I was on the loudspeaker going bananas about "This is an evacuation. I repeat: this is a full evacuation" and all that (I always LOVE it when people say "I repeat" and then they say it slightly differently from the first time lol!).
We've had troop-mobilisations and, as Oliver Norton said during the American Civil War: "Drill, then drill, then drill again". It's kept me on my toes organising all of this!
I found such a beautiful mountain. You'll just have to imagine it because I'm here and you're not. It was red at the bottom and red and blue at the top. It was taller than all the others but easier to climb because it doesn't have all those crumbling rocks. From it you could see the little three white mountains and the one green hill that looks like you're still on Earth. I stood there naked in the strong wind. You might have found it too cold but I didn't. I'm very strong.
* * * * * * * * * * *
It's happened. I'm so excited. Yesterday was the best day since I came, possibly the best day in my life. A spacecraft came within one Astronomical Unit of My World. It's only happened twice before and the others scarpered - you could practically feel the panic on their decks as they struggled desperately to manoeuvre away from me lol! That was good but this was the business: I'VE SHOT DOWN MY FIRST CRAFT! It was too good. I wish I could have that moment over and over again. I'll tell you something for nothing: that mirror got a good kissing after that!
I'm running ahead of myself - I'm too excited! I must calm down. Yes, basically this dirty great red ship came within range. The image of me was sent out automatically and alarms started going off all over My World. They ignored it - it was clearly some kind of battle cruiser. They sent a message back. Ugly brutes. Their captain was shouting stuff - probably obscenities. So we sent the second one, you know, the one of me in armour. He was spitting at it and brandishing some weapon in the one they sent back. I locked on to the 'com, though, so he couldn't switch it off. You should have seen his head going down, puzzled, as he tried to switch off the live image of me. You could almost hear him going, "What?" Then he looked up... and it was too late lol! You could actually see the red fiery flare glinting on the inside of their screen. They were all like "Crap!" and staring at this thing - they must have been going, "How do we get out of this?" Well you don't, mate - you don't. I suppose you've realised that now but it's a bit late! I teleported to the top of the mountain. You might have been scared but I wasn't. It was the very beginning of the Rainy Season (it rains for four months on this planet and you literally die because of the water pressure if you go out at the height of it - FUNNY!). The rain was already hard enough to tear at my flesh and there was blood and rain pouring down me and there was fire in the sky and bits of metal pouring down from where the spaceship got TOTALLY BURNT UP, ladies and gentlemen, I said TOTALLY BURNT UP lol! I was singing and dancing to one of my favourite of Cher's songs. You should have seen me dancing to it on the mountain top as the burning debris fell around me.
"Do you believe in life after love?
I can feel something inside me say
I really don't think you're strong enough, no.
Do you believe in life after love?"
It was QUALITY!


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Costume Information
|Cost :
|Time Taken :
|One week
|Everyone loves Phoenix, and no one gets his hair right. Myself included, though I had a good go at it.
Getting the suit colour right is very hard, I did well IMHO but it's not perfect, and the style is definitely off. The badge is made of sculpey and is a bit oversized.
The hair is FUNKY FOAM! Lovely stuff. The fringe isn't right but it gives a great impression of the back of his spiky hair. It also comes on and off in seconds, folds up without damaging the spikes for travel, and you can put it on other people ;)
We also had some wooden fold-out desks we could wheel around and slam hands on.. only, they didn't fit in the car. Oops.


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Added for emphasis to a question,or to show you are surprised or annoyed.
ex: What on earth is coming on?
Something is very expensive.
ex:My necklace cost the earth.
An event or a new is extremely shocking and important.
ex:The president is dead,it is earth-shattering.
You have plenty of time
ex: Take it easy,you have all the time in the world
Something is so good and unbelievable
ex:she is so beautiful,She is out of this world.
Something is extending throughout the entire world
ex:A worldwide epidemic
when you have great affection and respect for someone
ex:I love my parents,I think the world of them.
When you feel absolutely fantastic.
ex: I am getting married,I am on top of the world.
The place where people dance.
ex: They are on the dance floor.
It is the land at the bottom of the sea.
ex:There are plenty of weird fish at the ocean floor.
The planks of wood in a wooden floor
ex: They just floorboards to my house.
To be realistic and practical.
ex:He doesn't love you,you must keep your feet on the ground.
Someone is sad or depressed.
ex:I didn't get my schoolarship,I am so grounded.
When a plan or business starts to succed.
ex: My company just gets on the ground


text:
|Message view
|« Date » · « Thread »
|« Date » · « Thread »
|"Mark R. Diggory" <mdigg...@latte.harvard.edu>
|Re: cvs commit: jakarta-commons-sandbox/math/src/test/org/apache/commons/math/stat
|Mon, 16 Jun 2003 16:48:02 GMT
Al Chou wrote: >--- firstname.lastname@example.com wrote: > > >>mdiggory 2003/06/16 07:29:31 >> >> Modified: math/xdocs developers.xml >> math/src/java/org/apache/commons/math/stat >> UnivariateImpl.java >> math/src/test/org/apache/commons/math/stat >> CertifiedDataTest.java >> Log: >> PR: http://nagoya.apache.org/bugzilla/show_bug.cgi?id=20782 >> Submitted by: email@example.com >> >> I added this, but there are changes I'd like to make in the near future. >>Only the "running" aspects of the variance calc should be in the insertValue >>function, all other calculation should be in the getVariance function. >> >> > >OK, that sounds reasonable. Also, I was starting an Extract Method refactoring >to reduce duplication among the windowSize != n and infinite window branches of >insertValue. > > >Al > Yes, this is the direction I am working on as well. Lets try to coordinate our efforts. (1) I'm looking to setup "true deligation" where UnivariateImpl is actually an extension of AbstractStoreUnivariate and deligates to these methods when doing stored processing. This would simply look like: /** * @see org.apache.commons.math.stat.Univariate#getMean() */ public double getMean() { if (windowSize != Univariate.INFINITE_WINDOW) { return super.getMean(); } return mean; } (2) I want to apply the same strategy used in your mean and variance calculations for skew and kurt. The getters for these properties then would truely just be "getters" without the calculations occuring in them as well. This means the sum of powers code goes away for now. (3) I want to derive an methodology for the same two-pass algorithm for skew and kurt, hey, if we can't find published work on it, then theres a possibly paper in the future for someone to write! -Mark --------------------------------------------------------------------- To unsubscribe, e-mail: firstname.lastname@example.com For additional commands, e-mail: firstname.lastname@example.com
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This moisturizer has a great name and a lush, silky texture to comfort dry, sensitive skin -- too bad its formula contains enough problematic ingredients that sensitive, reddened skin may become worse, not better!
Several ingredients in this moisturizer are great for dry, sensitive skin. And no question this contains fewer plant-based irritants than what's typically seen in Decleor's moisturizers. But when sensitive, reddened skin is the concern you don't want to see any problematic ingredients, natural or synthetic. With this moisturizer, you're getting a mix of good and bad, yet your skin deserves (and in fact needs) only the good stuff!
Adding to the frustrating formulation is that many of the good plant ingredients won't remain stable and effective because this moisturizer is packaged in a jar. See More Info for details on why jar packaging is a problem. And check out our list of Best Sensitive Skin Products for superior, less expensive options.
One more comment: Decleor describes this as a day cream, but without sunscreen it is ill-suited for daytime use. The only difference between a day cream and a night cream is that the day cream should contain sunscreen and, of course, both should be well formulated and filled with antioxidants and skin-repairing and cell-communicating ingredients.
More Info:
The fact that this moisturizer is packaged in a jar means the beneficial ingredients won't remain stable once it is opened. All plant extracts, vitamins, antioxidants, and other state-of-the-art ingredients break down in the presence of air, so once a jar is opened and lets the air in, these important ingredients begin to deteriorate. Jars also are unsanitary because you're dipping your fingers into them with each use, adding bacteria which further deteriorate the beneficial ingredients (Sources: Free Radical Biology and Medicine, September 2007, pages 818-829; Ageing Research Reviews, December 2007, pages 271-288; Dermatologic Therapy, September-October 2007, pages 314-321; International Journal of Pharmaceutics, June 12, 2005, pages 197-203; Pharmaceutical Development and Technology, January 2002, pages 1-32; International Society for Horticultural Science, www.actahort.org/members/showpdf?booknrarnr=778_5; Beautypackaging.com; and www.beautypackaging.com/articles/2007/03/airless-packaging.php).
This high-tolerance day cream with a silky, melting and luxurious texture is specifically formulated to care for sensitive and normal to dry skins. Thanks to the "Lacto Calm" complex, together with protective and comforting plant active ingredients, it acts on the skin like a caress to help soothe and relieve feelings of discomfort and redness by tackling the source of the skin's fragility.
Water, Glycerin, Isononyl Isononanoate, Caprylic/Capric Triglyceride, Butylene Glycol, Pentylene Glycol, Cetearyl Alcohol, Dimethicone, Glycol Palmitate, Ribes Nigrum (Black Currant) Seed Oil, Squalane, Panthenol, Zea Mays (Corn) Oil, Rosa Damascena (Rose Hip) Flower Oil, Rosa Damascena Flower Extract, Moringa Pterygosperma Seed Extract, Boerhavia Diffusa Root Extract, Betula Alba Bark Extract, Scrophularia Nodosa Extract, Hydrolyzed Viola Tricolor Extract, Palmitoyl Grape Seed Extract, Palmitoyl Pine Bark Extract, Lilium Candidum Flower Extract, Rosmarinus Officinalis (Rosemary) Leaf Extract, Gossypium Herbaceum (Cotton) Seed Oil, Helianthus Annuus (Sunflower) Seed Oil, PEG-60 Hydrogenated Castor Oil, Dipropylene Glycol, Arachidyl Alcohol, Cetearyl Glucoside, Behenyl Alcohol, Cottonseed Oil/Palm Oil Aminopropanediol Esters, Arachidyl Glucoside, Polyacrylate-13, Polyisobutene, Maltodextrin, BHT, Tetrasodium EDTA, Glycolipids, Polysorbate 20, Sclerotium Gum, Glyceryl Stearate SE, Xanthan Gum, Ethylhexylglycerin, Fragrance (Parfum), Benzyl Salicylate, Butylphenyl Methylpropional, Linalool, Citronellol, Alpha-Isomethyl Ionone, Geraniol.
Decleor At-A-Glance
Strengths: None of note.
Weaknesses: Expensive; pervasive use of volatile essential oils that have limited to no benefit for skin and are known irritants; almost all the sunscreens lack the right UVA-protecting ingredients; no product to address acne or skin discolorations; inappropriate jar packaging.
What can you say about a skin-care line where almost 85% of the products contain volatile, fragrant plant oils that have research showing they are irritating to skin? Few lines in this book received so many unhappy faces for this reason alone—yet those very oils are Decleor's claim to fame. This spa-oriented company was begun in 1975 by a massage therapist and is now owned in part by Japan-based Shiseido (whose sunscreens trounce Decleor's by leaps and bounds).
Decleor is all about aromatherapy for skin. They speak freely of the purity of the essential oils they use and the distillation processes that keep them active, but that's precisely the cause for concern. Yes, lavender, bitter orange, rose, geranium, neroli, and other "essential" oils smell wonderful, but the very ingredients that create those intoxicating scents are what is responsible for causing skin irritation, inflammation, and, in some cases, phototoxic reactions. These essential oils have active constituents but, because they are not regulated as such, any company can use whichever ones they like in any concentration. Moreover, companies don't have to indicate the quantities that were used, leaving the consumer to guess. The concept of aromatherapy has well-established benefits concerning inhalation of scents and the effects they have on one's mood and, sometimes, physiological function. But enjoying these oils via inhalation (where they really can be beneficial) is different from applying them to skin, where hypersensitivity is well-documented and topical usage is cautioned (Sources: Current Pharmaceutical Design, December 2006, pages 3393–3399; Phytotherapy Research, September 2006, pages 758–763; European Journal of Oncology Nursing, April 2006, pages 140–149; The Journal of Nursing, August 2005, pages 11–15; and www.naturaldatabase.com).
Not only are most of Decleor's products a giant step backward for your skin, they're also a real misfortune when you consider Decleor's terrible sunscreens and lack of truly state-of-the-art ingredients. In short, experiencing these products in a relaxing spa environment may make you feel refreshed or invigorated—but if your goal is establishing a sensible, effective skin-care routine, you'll need to keep shopping.
For more information about Decleor, call (888) 414-4471 or www.decleor.com.
The Beautypedia and Paula's Choice Research teams have one mission: To help you find the best products for your skin, whether they're from Paula's Choice or another brand. By combining efforts, we're able to share scientific research and remain committed to the highest standards based on our decades of experience objectively reviewing thousands upon thousands of skincare and makeup formularies in all price ranges.
Beautypedia cuts through the hype to bring you product insights and recommendations you won't find anywhere else!


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3 American troops die in Afghanistan insider attack
Sun., Sept. 22, 2013, midnight
KABUL, Afghanistan – An Afghan wearing a security forces uniform turned his weapon against U.S. troops Saturday, killing three in eastern Afghanistan, officials said, in another apparent attack by a member of the Afghan forces against their international allies.
The shooting took place in Gardez, capital of eastern Paktia province, said Gen. Mohammad Zahir Azimi, an Afghan Defense Ministry spokesman. The area, near the border with Pakistan, has been a front line in fighting with the Taliban and other militants.
The attack took place inside a base of the Afghan army in the city, according to a security official in Gardez, who spoke on condition of anonymity because he was not authorized to give details while the incident was still under investigation.
A U.S. Defense Department official confirmed that all three soldiers were Americans, but that no further details would be released until after their relatives had been notified. NATO said the shooting was carried out by a gunman wearing the uniform of the Afghan National Security Forces, but it gave no further details.


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Steve Yendell
Posted - 15 April 2015
As a bosch afficionado this does everything i would have expected. Handy in tight spaces and as much power as you would need for most applications. Long battery run time too.
Godfrey Meese
Posted - 25 April 2014
Well familiar with the Bosch professional range, have used in the past, this is excellent for confined spaces and the best price to boot !.
Excellent free delivery and no hassle ordering.
Alexander Gardiner
Posted - 13 March 2014
We chose to buy from Power Tool world because of the price, but the service was excellent and the product of course is top quality. This little driver is now even more compact than before with the added benefit of the speed settings. It has improved torque setting as well. I loved the old version, but the new one is even better.


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1941 in Mandatory Palestine
From Wikipedia, the free encyclopedia
(Redirected from 1941 in the British Mandate of Palestine)
|This article does not cite any sources. (September 2010) (Learn how and when to remove this template message)
|1941 in the British Mandate of Palestine
Events in the year 1941 in the British Mandate of Palestine.
- High Commissioner - Sir Harold MacMichael
- Emir of Transjordan - Abdullah I bin al-Hussein
- Prime Minister of Transjordan - Tawfik Abu al-Huda
|This section needs expansion. You can help by adding to it. (August 2010)
- 15 May - The Palmach is established.
- 14 July - World War II: The Armistice of Saint Jean d'Acre (also known as the "Convention of Acre") is signed on at the "Sidney Smith Barracks" on the outskirts of the city of Acre, ending the Allied invasion of Vichy French-controlled Syria and Lebanon.
Notable births[edit]
- 11 February - Avraham Hirschson, Israeli politician
- 13 March - Mahmoud Darwish, Palestinian Arab poet and writer of prose (died 2008)
- 22 April - Amir Pnueli, Israeli computer scientist and Turing Award winner (died 2009)
- 7 July - Yisrael Poliakov, Israeli singer, actor and entertainer (died 2007)
- 13 July - Ehud Manor, Israeli songwriter, translator, and radio and TV personality (died 2005)
Notable deaths[edit]
|Wikimedia Commons has media related to 1941 in the British Mandate of Palestine.
- 20 May - David Raziel (born 1910), Russian-born Palestinian Jew, fighter of the Jewish underground and one of the founders of the Irgun
- 2 October - Menachem Ussishkin (born 1863), Russian-born Palestinian Jew, notable Zionist leader and chairman of the Jewish National Fund


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Gama Heritage Residency
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TravelPod Member ReviewsGama Heritage Residency Kochi
Very pleasant
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Travel Blogs from Kochi
On our last leg.
... 6 nations.
Our last evening we went to see some Kathakali dance, watching the men prepare their make-up, and a short demonstration of the moves used. The performance, telling a story from the Mabarahata was accompanied by 3 musicians on drums and voice. It was so fascinating, it was both tortuous and enjoyable. The stylised dance moves and intricate hand moves, together with some heroic gurning, eye-rolling ...
Kerala - Kochi, Alappuzha, Periyar & Trivandrum
... next stop was Alappuzha, a three hour train journey from Kochi, where operators compete to take you on tours around the backwaters on big houseboats. We opted for an overnight trip. The backwaters were traditionally used for transporting rice from the paddies on the edges of the water to villages and towns, which the boat took us drifting past. In the evening beers, Indian rum and cards came out, and ...
India Day 5
... an incredible experience to just stumble upon. After that I was SO glad we went with them. It was totally worth while...and such an awesome memory. We headed back to fort cochin and walked around in all the markets and got some wifi (yay) and then watched the sunset on the beach. Probably the most beautiful sunset I have seen thus far and I've seen lots! The whole sky was lite pink and we all sat and wrote in the sand as it set. Such an amazing way to end the day.
-Elle ...
Kochi and Mysore
... to go. It was surprisingly western. It was strange to be drinking cocktails in an expensive bar considering we were on a cramped bus with the locals only that morning. 99% of the people in the bar were Indian men (clearly with money) - where the hell are all the women in India? We were able to practice and learn some Indian dance move on the dance floor.
From Kochi we took our 5th overnight train via Bangalore (ie ...
Christmas in Kochi (Cochin) Kerala
... NO they both answered, still smiling and wobbling. You can't threaten somebody who doesn't understand the threat. So I counted out thirteen 500 Rupee notes and passed them to the Teaspoon Manager who had recently entered the negotiations. Then just as they were getting comfortable and putting the whole sorry affair behind them, I helped him count two of them back to me. That's the Indian way, I had paid in full therefore no sleight on his establishment or person had been received. I ...
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- Dreamy
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The International HotelP.B. No. 3563, M.G. Road, Kochi | 3 star hotelfrom $35
Mermaid HotelKaniyampuzha Road, Kochi | 3 star hotelfrom $28
Park CentralKaloor Kadavanthra Road, Kochi | 3 star hotelfrom $37
Casino Hotel\N, Kochi | 2 star hotelfrom $37
The Avenue RegentM.G. Road, Kochi | 3 star hotelfrom $54
Abad Atrium HotelM.G. Road, Kochi | 3 star hotelfrom $53
Bharat Hotel2357 Gandhi Square P B No, Kochi | 2 star hotelfrom $22
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Hotel PresidencyParamara Road, Kochi | Hotelfrom $39
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Belmore Court Motel5 Wickham Drive, Enniskillen | 4 star motelfrom $34
Hotel SAAS TowerCannon Shed Road, Near Main Boat Jetty, Kochi | 2 star hotelfrom $16
ATS Willingdon HotelWillingdon Island, Kochi | 2 star hotelfrom $24
The Capital Fort KochiV/40 Door No, Kochi | Hotelfrom $65
Gaanam HotelNear South Railway Junction, Kochi | 2 star hotelfrom $23
Grand Hotel CochinM.G. Road, Kochi | 3 star hotelfrom $58
Travancore Court HotelWarriam Road Kochi, Kochi | 3 star hotelfrom $51
- Travancore court hotel


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The Eye itself is the inner sanctum of Tempest Keep – the lair of Kael'thas Sunstrider and the heart of the teleporting fortress.
The mighty Tempest Keep was created by the enigmatic naaru: sentient beings of pure energy and the sworn enemies of the Burning Legion. In addition to serving as a base of operations for the naaru, the structure itself possesses the technology to teleport through alternate dimensions, traveling from one location to another in the blink of an eye.


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As Maine's premier 5-piece wedding band, Wavelength can play everything from ceremony, cocktail hour and dinner music to an unforgettable dance party. Tailored to your wedding style, the perfect musical element will compliment your special day from beginning to end. Whether your wedding reception is tented on private property or held at a seaside resort, your music choice will set the tone for an...
Copyright © 2001-2017 OneWed Inc.
All Rights Reserved.
Copyright © 2001-2017 OneWed Inc. All Rights Reserved.


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Three Choirs Late Harvest, Gloucestershire, England 2011 (£15.99, The Wine Pantry) Remember the miserable squib of a summer of 2012? It was, by all accounts, a bit of a disaster for English wine, and many producers struggled to make anything at all. A little local knowledge goes a long way however, and the UK's sole English wine specialist, The Wine Pantry, a tiny but brilliant independent wine merchant with an enviable position in London foodie centraal as you turn onto Stoney Street opposite Borough Market, has used theirs to good effect in sourcing a charming dry white from the vintage. The Signature blend from New Hall Vineyards in Purleigh near Chelmsford, Essex (£10.99) has a touch of Alsace in its brisk mix of citrus and blossom. Even better, however, is the honeyed peach of Three Choirs' sweet sticky siegerrebe, harvested late into the mercifully Indian part of the no-less tricky summer of 2011.
Biocantina Giannattasio Bombino Bianco, Puglia Italy 2012 (£15, Vini Italiani) Another relative newcomer to the burgeoning UK indie wine scene (it's just celebrated its second anniversary by opening a wine bar), Vini Italiani in South Kensington has given itself a broader palette to paint from than the Wine Pantry: Italy is the world's second-largest wine producer, England isn't even in the Top 40. Wheat-chaff separation is the name of the game, here, and what makes Vini Italiani stand out is their willingness to root out bottles from every corner of the country. That translates into delicious curiosities like the rarely seen (in the UK) dry white bombino from Puglia in the south, with its herbs, flowers, and lime so pure they could have been distilled. But it also means superior bottles from better-known regions, such as the joyously aromatic and succulent red Tenuta Lilliano Chianti Classico 2010 (£15).
Château Recougne Bordeaux Supérieur, France 2010 (£9.99, or £7.99 if you buy two bottles, Majestic) Bordeaux comes in for a lot of justified stick for the excessive prices and rather charmless, alienating air of stiff formality that comes with its top wines, and for the mealy-mouthed meanness of the bulk-bought stuff it tends to offer up in the supermarkets. But there's a lot more to what is, after all, one of the world's largest wine regions than those two extremes, particularly in better vintages like 2009 and 2010. For the two-bottle price of £7.99, Château Recougne's classic blend of merlot with the cabernets sauvignon and franc, with its juicy blackcurrant framed by trademark Bordelais freshness and gently gripping tannin, is hard to beat for value if you're looking for a crowd-pleasing partner for a Sunday roast.


text: A Conversation About Fuzzy Logic and Vagueness 1 ¨ ´ C HRISTIAN G. F ERM ULLER AND P ETR H AJEK ˇ ¨ Chris Fermuller: At the LoMoReVI conference, last September, in Cejkovice you gave an interesting presentation entitled Vagueness and fuzzy logic—can logicians learn from philosophers and can philosophers learn from logicians? . . . Petr H´ajek: . . . but I pointed out that my title in fact just added 'and can philosophers learn from logicians?' to a title of an earlier paper of yours! CF: I am flattered by this reference to my own work. But we should let our intended audience know a bit a more about the background of those two contributions. I still remember that I imagined to be quite bold and provocative by submitting a paper to a workshop on Soft Computing—organized by you, by the way, in 2003—that suggested already in the title that logicians should not just presume that the are properly dealing with vagueness when they investigate fuzzy logics, but should pay attention to the extended discourse on so-called 'theories of vagueness' in philosophy to understand the various challenges for correct reasoning in face of vagueness. I was really surprised when my submission was not only accepted, but when you even decided to make me an invited speaker, which entailed a longer presentation. A version of the contribution soon afterwards appeared as [7], again on your invitation. PH: Don't forget that I also want to ask the reverse question: 'Can philosophers learn from logicians?' I think that philosophers are often badly informed about what fuzzy logic in the narrow sense of formal development of many-valued calculi, often called just mathematical fuzzy logic, has to offer. CF: I agree with you, of course, but my original audience consisted people working in fuzzy logic. I saw no point in explaining to them how philosophers could profit from a better knowledge of their field. But the LoMoReVI conference was an excellent opportunity to ask the 'reverse question', since we had experts from quite different areas: logic, mathematics, cognitive science, linguistics, but also philosophy. So what are the main features of fuzzy logic, that you think philosophers should learn about? PH: First of all one should recall the distinction between fuzzy logic in the broad and in 1 Christian G. Ferm¨ uller was supported by the grant I143-G15 of the Austrian Science Foundation (FWF) Petr H´ajek was supported by the grant ICC/08/E018 of the Czech Science Foundation (both these grant are part of ESF Eurocores-LogICCC project FP006). Petr H´ajek also acknowledges the support of the Institutional Researc Plan AV0Z10300504. 406 Christian G. Ferm¨uller and Petr H´ajek the narrow sense as presented by several authors, among them Wang who writes in [25]: Fuzzy logic in the narrow sense is formal development of various logical systems of many-valued logic. In the broad sense it is an extensive agenda whose primary aim is to utilize the apparatus of fuzzy set theory for developing sound concepts, principles and methods for representing and dealing with knowledge expressed by statements in natural language. I want to focus on fuzzy logic in the narrow sense, often called just mathematical fuzzy logic. CF: Your monograph [13], published in 1998, has been and to a large extent still is the major source for research in mathematical fuzzy logic. In preparation for this conversation I checked the corresponding google.scholar entry, where it is currently listed as cited 2133 times—quite an achievement for a book entitled "Metamathematics of Fuzzy Logic" and that is certainly not a student textbook nor amounts to easy reading. I am glad that I had the chance to witness the evolution of its major concepts in the mid and late 1990's, when various collaborations, in particular also the COST Action 15 on "Many-valued Logics for Computer Applications", gave ample opportunity to present and discuss what one can call the t-norm based approach to deductive logic. Let us try to summarize the essential ingredients very briefly. PH: Well, a binary operation ∗ on the real unit interval [0, 1] is a t-norm if it is commutative (x ∗ y = y ∗ x), associative (x ∗ (y ∗ z) = (x ∗ y) ∗ z), non-decreasing in both arguments (x ≤ y implies x ∗ z ≤ y ∗ z and consequently z ∗ x ≤ z ∗ y), and where 1 is the unit element (x ∗ 1 = x). I suggest to consider any continuous t-norm as a candidate of a truth function for conjunction. CF: Sorry for interrupting already at this stage, but I think the intended general audience should take note of a few 'design decisions' that are implicit in choosing this starting point. First of all we have decided to consider not just 0 for 'false' and 1 for 'true' as formal truth values, but also all real numbers in between. In other words we have decided to allow for arbitrarily many intermediate truth values and insist that those values are densely linearly ordered. Moreover we stipulated that the semantics of conjunction as a logical connective can be modeled by some function over those 'degrees of truth'. This means that the semantic status of a conjunctive proposition A&B, i.e. its degree of truth depends only on the degrees assigned to A and B, respectively, but not on any material relation between the propositions A and B. In other words we stipulate truth functionality. This move alone implies that whatever 'degrees of truth' are, they must be something very different from 'degrees of belief' and from probabilities that certainly do not propagate functionally over conjunction. PH: Sure, but regarding the choice of [0, 1] as sets of truth value one should point that in investigations of mathematical fuzzy logic one frequently makes a move that is obvious to mathematicians, namely generalizing to algebraic structures that are less particular than [0, 1] equipped by the standard arithmetical operations and order. This gives the so-called general semantics of the logic in question. Regarding truth functionality, we A Conversation 407 can agree with the following critical statement of Gaifman [11]: There is no denying the graded nature of vague predicates—i.e. that the aptness of applying them can be a matter of degree—and there is no denying the gradual decrease in degree. More than other approaches degree theory does justice to these facts. But from this to the institution of many-valued logic, where connectives are interpreted as functions over truth degree there is a big jump. However, I want to point out that various detailed suggestions on how to deal with truth functionality have been made. For example, Jeff Paris [22] investigates conditions that justify truth functionality. Also the philosophers N.J.J. Smith in has monograph "Vagueness and Degrees of Truth" [24] on vagueness is positive on truth degrees and on truth functionality under some conditions. CF: Let us go further down the list of 'design choices' made by mathematical fuzzy logic. So far we have only mentioned possible truth functions of conjunction. But a considerable part of the mathematical beauty of the t-norm based approach that you have developed consists in the fact that one can derive truth function from all other logical connectives from given t-norms by quite straightforward assumptions on their relation to each other. PH: A central tenet of this approach is to observe that any continuous t-norm has a unique residuum that we may take as corresponding implication. This is derived from the principle that kA & Bk ≤ kCk if and only if kAk ≤ kB → Ck, where kXk denotes the truth value assigned to proposition X. Thus the truth function of implication is given by x → y = maxz {x ∗ z ≤ y}, where ∗ is the corresponding t-norm. Negation, in turn, can be defined by ¬A = A → ⊥, where ⊥ always receives the minimal truth value 0. Disjunction can be derived in various ways, e.g., by dualizing conjunction. Moreover, the popular choice of min for conjunction arises in two ways. First min is a one of three fundamental examples of a t-norm. The corresponding residual implication is given by kA → Bk = 1 for kAk ≤ kBk and kA → Bk = kBk otherwise. The corresponding truth function for disjunction, dual to conjunction (∨), is max, of course. This logic is called G¨odel logic in our community, because of one of those famous short notes of Kurt G¨odel from the 1930s, where he essentially defines these truth functions. But the logic is so fundamental that has been re-discovered and re-visited many times. Furthermore min as conjunction—or 'lattice conjunction' as our algebraically minded colleagues like to call it—arises in the t-norm based approach is the fact that it is definable in all those logics. i.e., even if we have chosen a another continuous t-norm as truth function for conjunction (&), min-conjunction (∧) is implicitly presented, e.g., by taking A ∧ B to abbreviate A & (A → B). In this sense all t-norm based logics—except G¨odel logics, of course—have two conjunctions. Having defined G¨odel logics explicitly, we should also mention two other fundamental logics: namely, Łukasiewicz logic, arising from the continuous t-norm a ∗ b = max(0, a + b − 1), and Product logic [16, 18], arising from standard multiplication over [0, 1] as underlying t-norm. Moreover, the three mentioned logics can be combined into a single system, called ŁΠ 21 [6]. 408 Christian G. Ferm¨uller and Petr H´ajek CF: But probably the most characteristic move that you have made in establishing t-norm based fuzzy logic as a rich research field is to ask: which logic arises if we do not fix any particular t-norm, but let conjunction vary over all continuous t-norms? You understandably call the resulting logic of all continuous t-norms "basic logic" [13, 4]. But since also other logics can and have been called "basic" in different contexts, it is best known as "H´ajek's BL" nowadays. In this context one should probably also mention the logic MTL [5], that arises if one generalizes continuity to left-continuity, which is still sufficient to guarantee the existence of unique residua for corresponding t-norms. We could indeed spend many hours discussing interesting and important results of mathematical fuzzy logic. At least one more basic fact should be mentioned: also first order versions, as well as various kinds of extensions, e.g., including modal operators, for the mentioned logics are well investigated by now. But we should return to our motivating question: can fuzzy logic contribute to theories of vagueness as investigated by philosophers? "Theories of Vagueness", as you know, is in fact the title of a book [20] by the philosopher Rosanna Keefe, who is very critical about degree based approaches to vagueness. I don't think that pointing out that Keefe has not been aware of contemporary developments in mathematical fuzzy logic when she wrote her book suffices to deflect the worries that she and others have voiced about fuzzy logic in this context. PH: Keefe characterizes the phenomena of vagueness quite neutrally focusing on socalled borderline cases, fuzzy boundaries, and susceptibility to the sorites paradox. I find it very acceptable, when she writes Vague predicates lack well-defined extensions. [They] are naturally described as having fuzzy, or blurred boundaries. Theorists should aim to find the best balance between preserving as many as possible of our judgments or opinions of various different kinds and meeting such requirements on theories as simplicity. There can be disputes about what is in the relevant body of opinions. Determining the counter-intuitive consequences of a theory is always a major part of its assessment. Regarding the intermediary truth values of fuzzy logic she writes later in [20]: . . . perhaps assignment of numbers in degree theory can be seen merely as a useful instrumental device. But what are we to say about the real truthvalue status of borderline case predictions? The modeler's approach is a mere hand waving . . . surely the assignment of numbers is central to it? Only order is important? My comment here is, that we can indeed say that truth degrees are just a "model": the task is not to assign concrete numerical values to given sentences (formulas); rather the task is to study the notion of consequence (deduction) in presence of imprecise predicates. One should not conflate the idea that, in modeling logical consequence and validity, we interpret statements over structures where formulas are evaluated in [0, 1] with the much stronger claim that we actually single out a particular such interpretation as the "correct" one, by assigning concrete values to atomic statements. A Conversation 409 CF: I see a rather fundamental methodological issue at play here. Philosophers often seem to suppose that any proposed theory of vagueness is either correct or simply wrong. Moreover, all basic features of a "correct" model arising from such a theory are required to correspond to some feature of the modeled part of "the real world". An exception to this general tendency is Stewart Shapiro, who in his book "Vagueness in Context" [23] has a chapter on the role of model theory, where he leaves room for the possibility that a model includes elements that are not intended to directly refer to any parameter of the modeled scenarios. Truth values from the unit interval are explicitly mentioned as an example. Nevertheless Shapiro finally rejects fuzzy logic based models of vagueness for other reasons. PH: In [14] I have taken Shapiro's book as a source for investigating some of the formal concepts he introduces in his contextualist approach to vagueness. No philosophical claims are made, but I demonstrate that Shapiro's model, that is based Kleene's three valued logic, can be rather straightforwardly generalized to BL as an underlying many valued logic. CF: As you indicate yourself, this leaves open the question how to interpret the role of intermediate truth values. After all truth values from [0, 1] or from some more general algebraic structure are the central feature of any fuzzy logic based model. PH: Let me point out an analogy with subjective probability here. By saying "Probably I will come" you assume that there is some concrete value of your subjective probability without feeling obliged to "assign" it to what you say. By the way, "probably" may be viewed as fuzzy modality, as explained in [13], Section 8.4, and in [12], as well as in many follow-up papers by colleagues. But, whereas the semantics of the logic of "probably" is specified truth functionally, probability itself of course is not truth functional. There is no contradiction here. Two levels of propositions are cleanly separated in the logic: the boolean propositions that refer to (crisp) sets of states measured by probabilities, and the fuzzy propositions that arise from identifying the probability of A with the truth value of "Probably A". CF: The analogy with subjective probability is indeed illuminating. It also provides an occasion to recall a central fact about logical models of reasoning that is shared with probability theory. Quite clearly, the aim is not to model actually observed behavior of (fallible) human reasoners in face of vague, fuzzy, or uncertain information. As is well known, human agents are usually not very good in drawing correct inferences from such data and often behave inconsistently and rather unpredictably when confronted with such tasks. While studying systematic biases and common pitfalls in reasoning under uncertainty and vagueness is a relevant topic in psychology with important applications, e.g., in economics and in medicine, the task of logic, like that of probability theory is quite different in this context: there is a strong prescriptive component that trumps descriptive adequateness. Thus, in proposing deductive fuzzy logic as a model of reasoning with vague expressions—at least of a certain type, namely gradable adjectives like "tall" or "expensive" when used in a fixed context—one does not predict that ordinary language 410 Christian G. Ferm¨uller and Petr H´ajek users behave in a manner that involves the assignment of particular values to elementary propositions or the computation of truth values for logically complex sentence using particular truth functions. Rather fuzzy logic (in the narrow sense) suggests that we obtain a formal tool that generalizes classical logic in a manner, that allows one to speak of preservation of degrees of truth in inference in a precise and systematic manner. Such tools are potentially useful in engineering contexts, in particular in information processing. Whether the resulting "models" are also useful in philosophy and linguistics is a different question. Linguists seem to be unhappy about a naive application of fuzzy logics, because empirical investigations suggest that no truth function matches the way in which speakers tend to evaluate logically complex sentences involving gradable or vague adjectives. (See, e.g., Uli Sauerland's and Galit Sasson's contributions to this volume.) Indeed, I think that, given the linguists' findings, truth functionality is best understood as a feature that it is prescribed, rather than "predicted" (to use a linguistic keyword). This actually already applies to classical logic. While we arguably ought to respect classical logic in drawing inferences, at least in realms like classical mathematics, logicians don't claim that ordinary language use of words like "and", "or", "implies", "for all" directly corresponds to the formal semantics codified in the corresponding truth tables, whether classical or many-valued. Note that, if I am right about the prescriptive aspect of logic, this does not at all exclude the usefulness of truth functional logics also in the context of descriptive models. However it implies that, in order to arrive at a more realistic formal semantics of vague natural language, fuzzy logic will certainly have to be supplemented by various intensional features and also by mechanism that model the dynamics of quickly shifting contexts, as described, e.g., by Shapiro [23] but also by many linguists investigating vagueness, e.g., [1]. Actually much work done in the context of LoMoReVI is of this nature, namely combining deductive fuzzy logics with other types of logical models. But then again, the role of classical logics in linguistics is analogous: it is routinely extended by intensional features, concepts from type theory and lambda calculus, generalized to so-called dynamic semantics, etc. Experts agree that there is no naive and direct translation from natural language into classical logic if we want to respect the apparent complexity of natural language expressions. Of course, the same applies to fuzzy logic. In any case, albeit the influential criticism of Kamp [19] and others, I'd say that the question of whether fuzzy logic can be usefully employed in linguistics is still open. PH: Your terms "prescribed" and "predicted" are new for me; I find them interesting but cannot say much about this distinction. I think that the relation of mathematical fuzzy logic to natural language is very similar to that of classical mathematical logic and its relation to natural language: both deal with symbolic sentences (formulas), not with sentences of a natural language. You say that the question of whether fuzzy logic can be usefully employed in linguistics is still open. My formulation would be "how far" instead of "whether" since I think that to some extent it has been shown already, e.g., by [24], that fuzzy logic can be usefully applied to the analysis of vague natural language. A Conversation 411 CF: Indeed, Nick Smith [24] develops a theory of vagueness that puts fuzzy logic in its very center. Although he mainly addresses his colleagues in philosophy, I agree that it is also of direct relevance to linguistics. However we have also mentioned that Rosanna Keefe in "Theories of Vagueness" [20] prominently criticizes an approach to vagueness that involves functions on degrees of truth as models for logical connectives. You have shortly discussed some of Keefe's objections in [15]. Since those objections are not only advanced by Keefe, but are rather widespread in philosophical discussions about fuzzy logic, I suggest to briefly look again into some concrete issues. PH: One of the things Keefe complains about—in the sense of judging it to be counterintuitive—is that, if A is a perfectly "half-true" proposition, i.e., if kAk = 0.5 then we have kA → Ak = kA → ¬Ak = 1, assuming the Łukasiewicz truth functions for implication (kA → Bk = min(1, 1 − kAk + kBk)) and negation (k¬Ak = 1 − kAk). But I think that this ceases to be problematic if we view a "half-true" statement as characterized by receiving the same truth value as its negation and remember that, like in classical logic, we declare kA → Bk to be 1 whenever kAk ≤ kBk. CF: Still, I understand why Keefe thinks that modeling implication in this way clashes with some intuitions about the informal meaning of "if . . . then . . . ". I guess that she would point out that it is hard to accept, previous to exposure to fuzzy logic, that "If it is cold then it is not cold" has the same semantic status as "If it is cold then it is cold" in a borderline context with respect to temperature. This, of course, is a consequence of truth functionality and of the rather innocent assumption that the truth value of a perfect "half-truth" is identical to that of its negation. I think that the reliance on pre-theoretic intuitions is at least as problematic here as it is in the case of the so-called paradoxes of material implication for classical logic. That the formula A → B is true according to classical logic, whenever A is false or B is true, only emphasizes the well known fact that there is a mismatch between (1) the precise formal meaning of → as stipulated by the corresponding truth function and (2) the conditions under which an utterance of the form "If . . . then . . . " successfully conveys information among speakers of English. We have to keep in mind that material implication is not supposed to refer to any content-related dependency between its arguments, but only refers to the (degrees of) truth of the corresponding sub-formulas. Your reply to Keefe's criticism points out that it is perfectly coherent to define the meaning of the connective "→" in the indicated manner, if we are prepared to abstract away from natural language and from pre-formal intuitions. The main motivation for doing so is to arrive at a mathematically robust and elegant realm of logics that we can study in analogy to classical logic, right? PH: Right. Let me once more emphasize that the metamathematics that arises from this particular generalization of classical logic is deep and beautiful indeed, as not only my book [13], but dozens, if not hundreds of papers in contemporary mathematical fuzzy logics can testify. 412 Christian G. Ferm¨uller and Petr H´ajek CF: I certainly agree. But this still leaves room for the possibility that mathematical fuzzy logic is just a niece piece of pure mathematics without much relevance for how we actually reason or should reason with vague notions and propositions. PH: Well, then let us consider some sentences from natural language that may illustrate some properties of fuzzy logic. Compare "I love you" with "I love you and I love you and I love you". Clearly the latter implies the former; but not necessarily conversely. If we model "and" by a nonidempotent t-norm then indeed a A is not equivalent to A&A, matching the indicated intuition. Moreover: "Do I like him? Oh, yes and no". Doesn't this mean that the truth value of "I like him" is neither 1 nor 0? Why shouldn't it be one half (0.5) in such a case? CF: You might remember from earlier conversations that I actually have a different opinion about these examples. Let me briefly spell it out here once more. As to repetition: I think that this is better analyzed as a pragmatic and not as a semantic phenomenon. To repeat a statement in the indicated manner is a way to emphasize the corresponding assertion. I don't think that conjunctive repetition in natural language entails the idea that the conjunction of identical statements may be less true than that the unrepeated statement. Note that linguists take it for granted that by asserting a declarative sentence S (in usual contexts) a speaker wants to convey that the proposition pS expressed by S is true in the given context. Emphasis, hesitation, doubt, etc., about pS may be expressed explicitly or implicitly by different means, but the impact of such qualifications should better not be conflated with the semantic status, i.e., the asserted truth of pS itself. As to "Yes and No": it is indeed not unusual to provide such an answer to the question whether (or to the suggestion that) a statement A holds. But it seems to me that this answer is a short form of expressing something like: "Yes, in some respect (i.e., in some relevant interpretation of the used words) A is indeed true; but in another, likewise relevant respect A is not true." If I am correct in this analysis, then degrees of truth do not enter the picture here. At least not in any direct manner. PH: What about hedges like "very", "relatively", "somewhat", "definitely" etc.? Extending standard first order fuzzy logics, one may consider, e.g., "very" as a predicate modifier. Syntactically this amounts to the stipulation that for every sentence P(a), where P is a fuzzy predicate and a is an individual, very(P)(a) is also a well-formed sentence. Semantically, the extension of the predicate very(P) is specified as a fuzzy set that can be obtained from the fuzzy set that represents the extension of the predicate P. This can be done in a simple and uniform manner, for example by squaring the membership function for P (µvery(P) (a) = (µP (a))2 . Obviously there is great flexibility in this approach and one can study the logic of such "truth stressers", and similarly "truth depressors", over given fuzzy logics, like BL or MTL, both proof theoretically and from an algebraic point of view (see, e.g., [2, 3]). A Conversation 413 CF: These are certainly good examples of research in contemporary fuzzy logic that is inspired by looking at words like "very", "relatively" etc. I have to admit that I am fascinated, but also a bit puzzled by the fact that one can retrieve literally hundreds of papers in fuzzy logic by searching for "linguistic hedges" in google.scholar. (Actually more than 27,100 entries are listed in total.) But if one looks at linguistic literature on the semantics of such words one finds quite different models. While gradability of adjectives and properties of corresponding order relations are investigated in this context, a methodological principle seems to be in place—almost universally accepted among linguists—that at the level of truth conditions one should stick with bivalent logic. I think that there are indeed good reasons, mostly left implicit, for sticking with this principle. If I understand linguists correctly, then a very important such reason is that their models should always be checked with respect to concrete linguistic data. But those data usually only allow to categorize linguistic expressions as being accepted or not accepted by competent language users. Indeed, it is hard to imagine how one could use a standard linguistic corpus to extract information about degrees of acceptability in connection with logical connectives. My remarks are not intended to imply that there can't be a role for fuzzy logic in linguistics. In recent work with Christoph Roschger [9] we explicitly talk about potential bridges between fuzzy logic and linguistic models. But these "bridges" do not directly refer to deductive t-norm based fuzzy logics. We rather looked at ways to systematically extract fuzzy sets from given contextual models, as they are used in so-called dynamic semantics. Of course, one could also generalize the underlying bivalent models to fuzzy ones. But the price, in terms of diminished linguistic significance, is hardly worth paying, unless one can show that mathematical structures arise that are interesting enough to be studied for their own sake. A direct role for logics like Łukasiewicz, G¨odel, Product logic, and more fundamental deductive fuzzy logics, like BL and MTL, in linguistic contexts may arise if we insist on the linguistic fact, that "true" itself is sometimes used as gradable adjective, just like "tall", "clever", "heavy" etc. The various fuzzy logics then correspond to (prescriptive) models of reasoning that take perfectly comprehensible talk about statements being only "somewhat true", "more true" than others, or "definitely true" at face value. Of course, we thereby abstract away from individual utterances and idealize actual language use in a manner that is familiar from classical logic. PH: Your last remark may bring us back to philosophy. There the sorites paradox is considered whenever one discusses the role of logic in reasoning with vague notions. In [17] an analysis of sorites is offered using a hedge At—"almost true". Consider the axioms: bold(0) and (∀n)(bold(n) → At(bold(n + 1))), where (bold(n) represents the proposition that a man with n hears on his head is bold. This is augmented by further natural axioms about At. Based on basic logic BL we obtain a simple and clear degree based semantics for At and for bold that does not lead to contradiction or to counterintuitive assumptions. CF: This is indeed a nice example of how fuzzy logic can be used as a prescriptive tool of reasoning. The paradox simply disappears, which of course implies that the model is not be understood descriptively. If people actually find themselves to be in a sorites like 414 Christian G. Ferm¨uller and Petr H´ajek scenario, they will feel the tendency to end up with contradicting assumptions. In other words they do not use fuzzy logic to start with. After all we ("competent speakers") do understand that such a scenario can is "paradoxical". Your models show that one can avoid or circumvent the difficulty by considering "near-truth" in a systematic manner. Shapiro [23] offers an alternative analysis that moves closer to observable behavior of speakers. He invites us to imagine a community of conversationalists that are successively confronted with members of a sorites series, e.g., a series of 1000 men, starting with Yul Brynner and ending with Steve Pinker, where each man is indistinguishable from his neighbors in the series in respect of boldness. Shapiro's model predicts, that if the conversationalists are forced to judge the boldness of each of those men one by one, they will try to maintain consistency with their earlier (yes/no) judgments. However at some point they will realize that this is not possible if they don't want to call Steve Pinker bold, which is absurd, as anyone that has ever seen a picture of Pinker can testify. Thus they will retract earlier judgments made along their forced march through the sorites series and thereby "jump" between different (partial) truth assignments. Shapiro uses precisification spaces based on Kleene's three valued logic to model the resulting concept of inference formally. As you have already mentioned, you have shown in [14] how Shapiro's model can be generalized to placing fuzzy instead of of a three valued interpretations at its core. In [8] I indicate that this can be understood as abstracting away from a concretely given sorites situation towards a model that summarizes in a static picture what can be observed about the overall dynamics of many individual instances of forced marches through a sorites series. In that interpretation degrees of truth emerge as measures of likelihood of "jumps", i.e., of revisions of binary judgments. Truth-functionality is preserved, because for complex statement we don't consider the likelihood of, say, judging A&B to be true, but rather the (properly regulated) degree of truth of the statement "A is likely to be judged true and B is likely to be judged true". (There is some similarity to the earlier mentioned logic of "probably" as a fuzzy modality.) PH: We should not give the wrong impression that fuzzy logic in its broader sense of dealing with problems and applications arising from a graded notion of membership in a set is mainly used to analyze vague language. The areas of fuzzy controlling, soft computing, and inference using "fuzzy if-then rules" have not only attracted a lot of research, but can point to many interesting applications in engineering, decision making, data mining, etc. (see, e.g., [25]). The simple idea to model an instruction like "If the pressure is rather high. then turn the valve slightly to left" by reference to fuzzy sets rather than to fixed threshold values has proved to be effective and useful. With hindsight it is hard to understand why Zadeh's proposal to generalize the classical notion of a set ("crisp set") to a fuzzy set by allowing intermediate degrees of membership [21] has been met with so much resistance from traditional mathematics and engineering. Presumably many found it unacceptable to declare that vagueness is not necessarily a defect of language, and that it may be adequate and useful to deal with it mathematically instead of trying to eliminate it. There is a frequently encountered misunderstanding here: fuzzy logic provides precise mathematical means to talk about impreciseness, but it does not advocate imprecise or vague mathematics. A Conversation 415 CF: As Didier Dubois in his contribution to this volume reminds us, Zadeh insisted that a proposition is vague if, in addition to being fuzzy, i.e., amenable to representation by fuzzy sets and relations, "it is insufficiently specific for a particular purpose" [26]. I am not sure that this characterization of vagueness is robust enough to assist useful formal models. But in any case, it is clear that fuzziness and vagueness are closely related and might not always be distinguishable in practice. At the very least there is some kind of dependency: fuzzy notions systematically give rise to vague language. PH: Let us finally return to our two-fold question: can logicians learn from philosophers and can philosophers learn from logicians? I think we both agree that the answer should be "yes". CF: Certainly. Moreover, thanks also to the activities in LoMoReVI and our sister LogICCC project VAAG, we may include linguists in the circle of mutual learning regarding appropriate theorizing about vagueness. BIBLIOGRAPHY [1] Barker C.: The dynamics of vagueness, Linguistics and Philosophy 25(1):1–36, 2002. [2] Bˇelohl´avek R., Funiokov´a T., and Vychodil V.: Fuzzy closure operators with truth stressers, Logic Journal of IGPL 13(5):503–513, 2005. [3] Ciabattoni A., Metcalfe G., and Montagna F.: Algebraic and proof-theoretic characterizations of truth stressers for MTL and its extensions. Fuzzy Sets and Systems 161(3):369–389, 2010. [4] Cignoli R.L.O., Esteva F., Godo L., and Torrens A.: Basic logic is the logic of continuous t-norms and their residua, Soft Computing 4:106–112, 2000. [5] Esteva F., Godo L.: Monoidal t-norm based logic, Fuzzy sets and systems 124:271–288, 2001. [6] Esteva F., Godo L., and Montagna F.: The ŁΠ and ŁΠ 12 logics: Two complete fuzzy systems joining Łukasiewicz and product logic', Archive for Mathematical Logic 40:39–67, 2001. [7] Ferm¨uller C.G.: Theories of vagueness versus fuzzy logic: can logicians learn from philosophers?', Neural Network World 13:455–465, 2003. [8] Ferm¨uller C.G.: Fuzzy logic and vagueness: can philosophers learn from Petr H´ajek? In P. Cintula, ˇ Z. Hanikov´a, and V. Svejdar (eds.), Witnessed Years: Essays in Honour of Petr H´ajek, College Publications, 373–386, 2009. [9] Ferm¨uller C.G. and Roschger C.: Bridges Between Contextual Linguistic Models of Vagueness and T-norm Based Fuzzy Logic. In T. Kroupa, J. Vejnarova (eds.), Proceedings of 8th WUPES, 69–79, 2009. [10] Fine K.: Vagueness, truth and logic. Synthese 30:265–300, 1975. [11] Gaifman H.: Vagueness, tolerance and contextual logic. Synthese 174:5–46, 2010. [12] Godo L., Esteva F., and H´ajek P.: Reasoning about probability using fuzzy logic, Neural Network World 10(5):811–824, 2000. [13] H´ajek P.: Metamathematics of Fuzzy Logic, Kluwer, 1998. [14] H´ajek P.: On Vagueness, Truth Values and Fuzzy Logics. Studia Logica 91:367–382, 2009. [15] H´ajek P.: Deductive systems of fuzzy logic. A. Gupta, R. Parikh, and J. van Benthem (eds.), Logic at the crossroads: an interdisciplinary view, 60–74. Allied publishers PVT, New Delhi 2007. [16] H´ajek P., Esteva F., and Godo L.: A complete many-valued logic with product conjunction. Archive for Mathematical Logic 35:198–208, 1996. [17] H´ajek P., Nov´ak V.: The Sorites paradox and fuzzy logic, Int. J. of General Systems 32:373–383, 2003. [18] Horˇc´ık R., Cintula P.: Product Łukasiewicz logic, Arch. Math. Log. 43:477–503, 2004. [19] Kamp H.: Two theories of adjectives. In Edward Keenan (eds.) Formal Semantics of Natural Languages. Cambridge University Press, 1975. [20] Keefe R.: Theories of Vagueness, Cambridge University Press, 2000. 416 Christian G. Ferm¨uller and Petr H´ajek [21] Klir G.J., Yuan B., (eds.) Fuzzy sets, fuzzy logic and fuzzy systems: Selected papers by Lotfi A. Zadeh. World Scientific Singapore 1996. [22] Paris J.B.: The uncertain reasoner's companion: a mathematical perspective. Cambridge Tracts in Theoretical Computer Science 39, Cambridge University Press, 1994. [23] Shapiro S.: Vagueness in Context, Oxford University Press, 2006. [24] Smith N.J.J.: Vagueness and truth degrees Oxford Uiv. Press 2008 [25] Wang P., Da Ruan, and Kerre E.E. (eds.): Fuzzy logic – a spectrum of theoretical and practical issues. Springer 2007. [26] Zadeh L.A.: PRUF—a meaning representation language for natural languages. International Journal of Man-Machine Studies 10(4):395–460, 1978. Christian G. Ferm¨uller Vienna University of Technology Favoritenstr. 9–11/E1852 A-1040 Wien, Austria Email: [email protected] Petr H´ajek Institute of Computer Science Academy of Sciences of the Czech Republic Pod Vod´arenskou vˇezˇ´ı, 2 182 07 Prague, Czech Republic Email: [email protected]


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