## 1. Introduction




The frame problem originated as a narrowly defined technical problem
in
 logic-based artificial intelligence
 (AI).
But it was taken up in an embellished and modified form by
philosophers of mind, and given a wider interpretation. The tension
between its origin in the laboratories of AI researchers and its
treatment at the hands of philosophers engendered an interesting
and sometimes heated debate in the 1980s and 1990s.
But since the narrow, technical problem is largely solved, recent
discussion has tended to focus less on matters of interpretation and
more on the implications of the wider frame problem for 
 cognitive science.
To gain an understanding of the issues,
this article will begin with a look at the frame problem in its
technical guise. Some of the ways in which philosophers have
re-interpreted the problem will then be examined. The article
will conclude with an assessment of the significance of the frame
problem today.


## 2. The Frame Problem in Logic




Put succinctly, the frame problem in its narrow, technical form is
this (McCarthy & Hayes 1969). Using mathematical logic, how is it
possible to write formulae that describe the effects of actions without
having to write a large number of accompanying formulae that describe
the mundane, obvious non-effects of those actions? Let's take a look at
an example. The difficulty can be illustrated without the full
apparatus of formal logic, but it should be borne in mind that the
devil is in the mathematical details. Suppose we write two formulae,
one describing the effects of painting an object and the other
describing the effects of moving an object.


1. *Colour*(*x*, *c*) holds after
*Paint*(*x*, *c*)
2. *Position*(*x*, *p*) holds after
*Move*(*x*, *p*)




Now, suppose we have an initial situation in which
*Colour*(*A*, *Red*)
and *Position*(*A*, *House*) hold. According to
the machinery of deductive logic, what then holds after the action
*Paint*(*A*, *Blue*) followed by the
action *Move*(*A*, *Garden*)? Intuitively, we
would expect *Colour*(*A*, *Blue*) and
*Position*(*A*, *Garden*) to hold. Unfortunately,
this is not the case. If written out more formally in classical
predicate logic, using a suitable formalism for representing time and
action such as the situation calculus (McCarthy & Hayes 1969), the
two formulae above only license the conclusion
that *Position*(*A*, *Garden*) holds. This is
because they don't rule out the possibility that the colour of
*A* gets changed by the *Move* action.




The most obvious way to augment such a formalisation so that the
right common sense conclusions fall out is to add a number of formulae
that explicitly describe the non-effects of each action. These formulae
are called *frame axioms*. For the example at hand, we need a
pair of frame axioms.


3. *Colour*(*x*, *c*) holds after *Move*(*x*, *p*) if *Colour*(*x*, *c*) held
beforehand
4. *Position*(*x*, *p*) holds after *Paint*(*x*, *c*) if *Position*(*x*, *p*) held
beforehand




In other words, painting an object will not affect its position, and
moving an object will not affect its colour. With the addition of these
two formulae (written more formally in predicate logic), all the
desired conclusions can be drawn. However, this is not at all a
satisfactory solution. Since *most* actions do not affect
*most* properties of a situation, in a domain comprising
*M* actions and *N* properties we will, in general, have
to write out almost *MN* frame axioms. Whether these formulae
are destined to be stored explicitly in a computer's memory, or are
merely part of the designer's specification, this is an unwelcome
burden.




The challenge, then, is to find a way to capture the non-effects of
actions more succinctly in formal logic. What we need, it seems, is
some way of declaring the general rule-of-thumb that an action can be
assumed not to change a given property of a situation *unless*
there is evidence to the contrary. This default assumption is known as
the *common sense law of inertia*. The (technical) frame problem
can be viewed as the task of formalising this law.




The main obstacle to doing this is the *monotonicity* of
classical logic. In classical logic, the set of conclusions that can be
drawn from a set of formulae always *increases* with the
addition of further formulae. This makes it impossible to express a
rule that has an open-ended set of exceptions, and the common sense law
of inertia is just such a rule. For example, in due course we might
want to add a formula that captures the exception to Axiom 3 that
arises when we move an object into a pot of paint. But our not having
thought of this exception before should not prevent us from applying
the common sense law of inertia and drawing a wide enough set of
(defeasible) conclusions to get off the ground.




Accordingly, researchers in logic-based AI have put a lot of effort
into developing a variety of *non-monotonic* reasoning
formalisms, such as *circumscription* (McCarthy 1986), and
investigating their application to the frame problem. None of this has
turned out to be at all straightforward. One of the most troublesome
barriers to progress was highlighted in the so-called *Yale shooting
problem* (Hanks & McDermott 1987), a simple scenario that gives
rise to counter-intuitive conclusions if naively represented with a
non-monotonic formalism. To make matters worse, a full solution needs
to work in the presence of concurrent actions, actions with
non-deterministic effects, continuous change, and actions with indirect
ramifications. In spite of these subtleties, a number of solutions to
the technical frame problem now exist that are adequate for logic-based
AI research. Although improvements and extensions continue to be found,
it is fair to say that the dust has settled, and that the frame
problem, in its technical guise, is more-or-less solved (Shanahan
1997; Lifschitz 2015).


## 3. The Epistemological Frame Problem




Let's move on now to the frame problem as it has been re-interpreted
by various philosophers. The first significant mention of the frame
problem in the philosophical literature was made by Dennett (1978,
125). The puzzle, according to Dennett, is how "a cognitive
creature ... with many beliefs about the world" can update
those beliefs when it performs an act so that they remain
"roughly faithful to the world"? In *The Modularity of
Mind*, Fodor steps into a roboticist's shoes and, with the frame
problem in mind, asks much the same question: "How ... does
the machine's program determine which beliefs the robot ought to
re-evaluate given that it has embarked upon some or other course of
action?" (Fodor 1983, 114).




At first sight, this question is only impressionistically related to
the logical problem exercising the AI researchers. In contrast to the
AI researcher's problem, the philosopher's question isn't
expressed in
the context of formal logic, and doesn't specifically concern the
non-effects of actions. In a later essay, Dennett acknowledges the
appropriation of the AI researchers' term (1987). Yet he goes on to
reaffirm his conviction that, in the frame problem, AI has discovered
"a new, deep epistemological problem--accessible in
principle but unnoticed by generations of philosophers".




The best way to gain an understanding of the issue is to imagine
being the designer of a robot that has to carry out an everyday task,
such as making a cup of tea. Moreover, for the frame problem
to be neatly highlighted, we must confine our thought experiment to a
certain class of robot designs, namely those using explicitly
stored, sentence-like representations of the world, reflecting the
methodological tenets of *classical AI*. The AI researchers
who tackled the original frame problem in its narrow, technical guise
were working under this constraint, since logic-based AI is a variety of
classical AI. Philosophers sympathetic to the
 computational theory of mind--who 
suppose that mental states comprise sets of
propositional attitudes and mental processes are forms of inference
over the propositions in question--also tend to feel at home
with this prescription.




Now, suppose the robot has to take a tea-cup from the cupboard. The
present location of the cup is represented as a sentence in its
database of facts alongside those representing innumerable other
features of the ongoing situation, such as the ambient temperature, the
configuration of its arms, the current date, the colour of the tea-pot,
and so on. Having grasped the cup and withdrawn it from the cupboard,
the robot needs to update this database. The location of the cup has
clearly changed, so that's one fact that demands revision. But which
other sentences require modification? The ambient temperature is
unaffected. The location of the tea-pot is unaffected. But if it so
happens that a spoon was resting in the cup, then the spoon's new
location, inherited from its container, must also be updated.




The epistemological difficulty now discerned by philosophers is this.
How could the robot limit the scope of the propositions
it must reconsider in the light of its actions? 
In a sufficiently simple robot, this doesn't seem like much of a
problem. Surely the robot can simply examine its entire database of
propositions one-by-one and work out which require modification. But
if we imagine that our robot has near human-level intelligence, and is
therefore burdened with an enormous database of facts to examine every
time it so much as spins a motor, such a strategy starts to look
computationally intractable.





Thus,
a related issue in AI has been dubbed the *computational aspect* of
the frame problem (McDermott 1987). This is the question of how to compute
the consequences of an action without the computation having to range
over the action's non-effects. The solution to the computational aspect
of the frame problem adopted in most symbolic AI programs is some
variant of what McDermott calls the "sleeping dog" strategy
(McDermott 1987). The idea here is that not every part of the data
structure representing an ongoing situation needs to be examined when
it is updated to reflect a change in the world. Rather, those parts
that represent facets of the world that have changed are modified, and
the rest is simply left as it is (following the dictum "let
sleeping dogs lie").
In our example of the robot and the tea-cup, we might apply the
sleeping dog strategy by having the robot update its beliefs about the
location of the cup and the contents of the cupboard. But the robot
would not worry about some possible spoon that may or may not be on or
in the cup, since the robot's goal did not directly involve any spoon.






However, the philosophical problem is not exhausted by this
computational issue. The outstanding philosophical question is how the
robot could ever determine that it had successfully revised all its
beliefs to match the consequences of its actions. Only then would it
be in a position safely to apply the "common sense law of
inertia" and assume the rest of the world is untouched. Fodor
suggestively likens this to "Hamlet's problem: when to stop
thinking" (Fodor 1987, 140). The frame problem, he claims, is
"Hamlet's problem viewed from an engineer's perspective".
So construed, the obvious way to try to avoid the frame problem is by
appealing to the notion of *relevance*. Only certain properties
of a situation are relevant in the context of any given action, so the
counter-argument goes, and consideration of the action's consequences
can be conveniently confined to those.




However, the appeal to relevance is unhelpful. For the difficulty now
is to determine what is and what isn't relevant, and this is dependent
on context. Consider again the action of removing a tea-cup from the
cupboard. If the robot's job is to make tea, it is relevant that this
facilitates filling the cup from a tea-pot. But if the robot's task
is to clean the cupboard, a more relevant consequence is the
exposure of the surface the cup was resting on.
An AI researcher in the classical mould could rise to this challenge
by attempting to specify what propositions are relevant to what context.
But philosophers such as Wheeler (2005; 2008), taking their cue from
Dreyfus (1992), perceive the threat of infinite regress here. As Dreyfus
puts it, "if each context can be recognized only in terms of features
selected as relevant and interpreted in a broader context, the AI worker
is faced with a regress of contexts" (Dreyfus 1992, 289).




One way to mitigate the threat of infinite regress is by appeal to the
fact that, while humans are more clever than today's robots,
they still make mistakes (McDermott 1987). People often fail to foresee
every consequence of their actions *even though* they lack none
of the information required to derive those consequences, as any novice
chess player can testify. Fodor asserts that "the frame problem
goes very deep; it goes as deep as the analysis of rationality"
(Fodor 1987). But the analysis of rationality can accommodate the
boundedness of the computational resources available to derive relevant
conclusions (Simon 1957; Russell & Wefald 1991; Sperber &
Wilson 1996). Because it sometimes jumps to premature conclusions,
bounded rationality is logically flawed, but no more so than human
thinking.
However, as Fodor points out, appealing to human limitations
to justify the imposition of a heuristic boundary on the kind of
information available to an inferential process does not in itself solve
the epistemological frame problem (Fodor 2000, Ch.2; Fodor 2008, Ch.4; see also Chow 2013).
This is because it neglects the issue
of how the heuristic boundary is to be drawn, which is to say it
fails to address the original question of how to specify what is and
isn't relevant to the inferential process.




Nevertheless, the classical AI researcher, convinced that the regress of
contexts will bottom out eventually, may still elect to pursue the research
agenda of building systems based on rules for determining relevance,
drawing inspiration from the past successes of classical AI.
Whereupon the dissenting philosopher might point out that AI's past
successes have always been confined to narrow domains, such as playing chess,
or reasoning in limited microworlds where the set of potentially relevant
propositions is fixed and known in advance. By contrast, human intelligence
can cope with an open-ended, ever-changing set of contexts (Dreyfus 1992;
Dreyfus 2008; Wheeler 2005; Wheeler 2008; Rietveld 2012).
Furthermore, the classical AI researcher is vulnerable to
an argument from holism. A key claim in Fodor's work is that when it
comes to circumscribing the consequences of an action, just as in the business
of theory confirmation in science, anything could be relevant (Fodor
1983, 105). There are no *a priori* limits to the properties
of the ongoing situation that might come into play. Accordingly, in his
modularity thesis, Fodor uses the frame problem to bolster the view
that the mind's central processes--those that are involved in
fixing belief--are "informationally unencapsulated",
meaning that they can draw on information from any source (Fodor 1983;
Fodor 2000; Fodor 2008; Dreyfus 1991, 115-121; Dreyfus 1992, 258).
For Fodor, this is a fundamental barrier to the provision of a
computational account of these processes.




It is tempting to see Fodor's concerns as resting on a fallacious
argument to the effect that a process must be informationally encapsulated
to be computationally tractable. We only need to consider the
effectiveness of Internet search engines to see that, thanks to clever
indexing techniques, this is not the case. Submit any pair of seemingly
unrelated keywords (such as "banana" and
"mandolin") to a Web search engine, and in a fraction of a
second it will identify every web page, in a database of several
billion, that mentions those two keywords (now including this page, no
doubt). But this is not the issue at hand. The real issue, to reiterate
the point, is one of relevance. A process might indeed be able to index
into everything the system knows about, say, bananas and mandolins, but
the purported mystery is how it could ever work out that, of all things,
bananas and mandolins were relevant to its reasoning task in the first
place.




To summarize, it is possible to discern an epistemological frame
problem, and to distinguish it from a computational counterpart. The
epistemological problem is this: How is it possible for holistic,
open-ended, context-sensitive relevance to be captured by a set of
propositional, language-like representations of the sort used in
classical AI? The *computational* counterpart to the
epistemological problem is this. How could an inference process
tractably be confined to just what is relevant, given that relevance
is holistic, open-ended, and context-sensitive?


## 4. The Metaphysics of Common Sense Inertia




An additional dimension to the frame problem is uncovered in (Fodor
1987), where the metaphysical justification for the common sense law of
inertia is challenged. Although Fodor himself doesn't clearly
distinguish this issue from other aspects of the wider frame problem,
it appears on examination to be a separate philosophical conundrum.
Here is the argument. As stated above, solutions to the logical frame
problem developed by AI researchers typically appeal to some version of
the common sense law of inertia, according to which properties of a
situation are assumed by default not to change as the result of an
action. This assumption is supposedly justified by the very observation
that gave rise to the logical frame problem in the first place, namely
that most things don't change when an action is performed or an event
occurs.




According to Fodor, this metaphysical justification is unwarranted.
To begin with, some actions change many, many things. Those who affirm
that painting an object has little or no effect on most properties of
most of the objects in the room are likely to concede that detonating a
bomb actually does affect most of those properties. But a deeper
difficulty presents itself when we ask what is meant by "most
properties". What predicates should be included in our ontology
for any of these claims about "most properties" to fall
out? To sharpen the point, Fodor introduces the concept of a
"fridgeon". Any particle is defined as a *fridgeon*
at a given time if and only if Fodor's fridge is switched on at that
time. Now, it seems, the simple act of turning Fodor's fridge on or off
brings about an astronomical number of incidental changes. In a
universe that can include fridgeons, can it really be the case that
most actions leave most things unchanged?




The point here is not a logical one. The effect on fridgeons of
switching Fodor's fridge on and off can concisely be represented
without any difficulty (Shanahan 1997, 25). Rather, the point is
metaphysical. The common sense law of inertia is only justified in the
context of the right ontology, the right choice of objects and
predicates. But what is the right ontology to make the common sense law
of inertia work? Clearly, fridgeons and the like are to be excluded.
But what metaphysical principle underpins such a decision?




These questions and the argument leading to them are very
reminiscent of Goodman's treatment of induction (Goodman 1954).
Goodman's
 "new riddle of induction",
 commonly called the *grue paradox*,
invites us to consider the predicate *grue*, which is true
before time *t* only of objects that are green and after time
*t* only of objects that are blue. The puzzle is that every
instance of a green emerald examined before time *t* is also an
instance of a grue emerald. So, the inductive inference that all
emeralds are grue seems to be no less legitimate than the inductive
inference that all emeralds are green. The problem, of course, is the
choice of predicates. Goodman showed that inductive inference only
works in the context of the right set of predicates, and Fodor
demonstrates much the same point for the common sense law of
inertia.




An intimate relationship of a different kind between the frame
problem and the problem of induction is proposed by Fetzer (1991), who
writes that "The problem of induction [is] one of justifying some
inferences about the future as opposed to others. The frame problem,
likewise, is one of justifying some inferences about the future as
opposed to others. The second problem is an instance of the
first." This view of the frame problem is highly controversial,
however (Hayes 1991).


## 5. The Frame Problem Today




The narrow, technical frame problem generated a great deal of work
in logic-based artificial intelligence in the late 1980s and early 1990s,
and its wider philosophical implications came to the fore at around the
same time. But the importance each thinker accords to the frame problem
today will typically depend on their stance on other matters.




Within classical AI, a variety of workable solutions to the logical
frame problem have been developed, and it is no longer considered a
serious obstacle even for those working in a strictly logic-based
paradigm (Shanahan 1997; Reiter 2001; Shanahan 2003; Lifschitz 2015).
It's worth
noting that logically-minded AI researchers can consistently retain
their methodology and yet, to the extent that they view their products
purely as engineering, can reject the traditional cognitive
scientist's belief in the importance of computation over
representations for understanding the mind. Moreover, insofar as the
goal of classical AI is not computers with human-level intelligence,
but is simply the design of better and more useful computer programs,
it is immune to the philosophical objections of Fodor, Dreyfus, and
the like. Significantly though, for AI researchers working outside
the paradigm of symbolic representation altogether--those
working in situated robotics, for example--the logical frame
problem simply doesn't feature in day-to-day investigations.




Although it can be argued that it arises even in a
 connectionist setting (Haselager &
Van Rappard 1998; Samuels 2010), the frame problem inherits much of its
philosophical significance from the classical assumption of the
explanatory value of computation over representations, an assumption
that has been under vigorous attack for some time (Clark 1997; Wheeler
2005). Despite this, many philosophers of mind, in the company of
Fodor and Pylyshyn, still subscribe to the view that human mental
processes consist chiefly of inferences over a set of propositions,
and that those inferences are carried out by some form of computation.
To such philosophers, the epistemological frame problem and its
computational counterpart remain a genuine threat.


 For Wheeler and others, classical AI and cognitive science rest on
Cartesian assumptions that need to be overthrown in favour of a more
Heideggerian stance before the frame problem can be overcome (Dreyfus
2008; Wheeler 2005; 2008; Rietveld 2012). According to Wheeler (2005;
2008), the situated robotics movement in AI that originated with the
work of Brooks (1991) exemplifies the right way to go. Dreyfus is in
partial agreement, but contends that the early products of situated
robotics "finesse rather than solve the frame problem"
because "Brooks's robots respond only to fixed isolable features
of the environment, not to context or changing significance"
(Dreyfus 2008, 335). Dreyfus regards the neurodynamics work of
Freeman (2000) as a better foundation for the sort of Heideggerian
approach to AI in which the frame problem might be dissolved (see also
Shanahan 2010, Ch.5; Rietveld 2012; Bruineberg & Rietveld
2014). Dreyfus is impressed by Freeman's approach because the
neurodynamical record of significance is neither a representation nor
an association, but (in dynamical systems terms) "a repertoire
of attractors" that classify possible responses, "the
attractors themselves being the product of past experience"
(Dreyfus 2008, 354).




One philosophical legacy of the frame problem is that it has drawn
attention to a cluster of issues relating to holism, or so-called
informational unencapsulation.
Recall that a process is informationally unencapsulated (Fodor sometimes
uses the term "isotropic") if there is no *a priori*
boundary to what information is relevant to it.
In recent writing, Fodor uses the term "frame
problem" in the context of all informationally unencapsulated
processes, and not just those to do with inferring the consequences
of change (Fodor 2000, Ch.2; Fodor 2006, Ch.4).
It's clear that idealised rationality is informationally
unencapsulated, in this sense.
It has also been suggested that isotropy is damaging to the so-called
 theory theory
 of folk psychology (Heal 1996).
(For Heal, this lends support to the rival
 simulation theory,
 but Wilkerson (2001) argues that informational unencapsulation is a
problem for both accounts of folk psychology.)
Analogical reasoning, as Fodor says, is an example of "isotropy
in the purest form: a process which depends precisely upon the transfer
of information among cognitive domains previously assumed to be
irrelevant" (Fodor 1983, 105).
Arguably, a capacity for analogical and metaphorical
thinking--a talent for creatively transcending the boundaries
between different domains of understanding--is the source of
human cognitive prowess (Lakoff & Johnson 1980; Mithen 1996). So
the informational unencapsulation of analogical reasoning is potentially
very troublesome, and especially so for modular theories of mind in which
modules are viewed as (context-insensitive) specialists
(Carruthers 2003; 2006).


 Dreyfus claims that this "extreme version of the frame
problem" is no less a consequence of the Cartesian assumptions
of classical AI and cognitive science than its less demanding
relatives (Dreyfus 2008, 361). He advances the view that a suitably
Heideggerian account of mind is the basis for dissolving the frame
problem here too, and that our "background familiarity with how
things in the world behave" is sufficient, in such cases, to
allow us to "step back and figure out what is relevant and
how". Dreyfus doesn't explain how, given the holistic,
open-ended, context-sensitive character of relevance, this
figuring-out is achieved. But Wheeler, from a similarly Heideggerian
position, claims that the way to address the
"inter-context" frame problem, as he calls it, is with a
dynamical system in which "the causal contribution of each
systemic component partially determines, and is partially determined
by, the causal contributions of large numbers of other systemic
components" (Wheeler 2008, 341). A related proposal is put
forward by Shanahan and Baars (2005; see also Shanahan 2010, Ch.6),
based on global workspace theory (Baars 1988), according to which the
brain incorporates a solution to the problem of informational
unencapsulation by instantiating an architecture in which a) the
responsibility for determining relevance is not centralised but is
distributed among parallel specialist processes, and b) a serially
unfolding global workspace state integrates relevant contributions
from multiple domains.