�Φ⌝)⌝= ⌜Φ⌝ [T (⌜Φ⌝)]1 ∆1 ⊥ ¬I,1¬T (⌜Φ⌝) T I T (⌜¬T (⌜Φ⌝)⌝) = E T (⌜Φ⌝) Then, we have the closed derivation ∆3 of ⊥. [T (⌜Φ⌝)]1 ∆1 ⊥ ¬I,1¬T (⌜Φ⌝) ∆2 T (⌜Φ⌝) ¬E⊥ 48 Claim 2. ∆3 generates a non-terminating reduction sequence, and so is not normalizable. ∆3 is not in normal form since it has a maximum formula ¬T (⌜Φ⌝). By applying ▷¬ to ∆3, we have the following derivation ∆4. Ax1⌜Φ⌝= ⌜¬T (⌜Φ⌝)⌝ Ax2⌜¬T (⌜Φ⌝)⌝= ⌜Φ⌝ [T (⌜Φ⌝)]1 ∆1 ⊥ ¬I,1¬T (⌜Φ⌝) T I T (⌜¬T (⌜Φ⌝)⌝) = E T (⌜Φ⌝) = E T (⌜¬T (⌜Φ⌝)⌝) T E¬T (⌜Φ⌝) ∆2 T (⌜Φ⌝) ¬E⊥ The application of ⊵Sub and ▷T (x) yield the same derivation with ∆3. Hence, the reduction procedure generates non-terminating reduction sequences and so it is not normalizable. According to TCPE, ∆3 is a T-paradox. If the Liar paradox is a genuine paradox and the nonterminating reduction sequence is the main feature of the genuine paradox, ∆3 supports the view that TCPE is
� Φ ⌝) ⌝ = ⌜ Φ ⌝ [ T (⌜ Φ ⌝ )]1 ∆1 ⊥ ¬I,1¬T (⌜ Φ ⌝) T I T (⌜ ¬T (⌜ Φ ⌝) ⌝) = E metric ton (⌜ Φ ⌝) Then, we take the closed derivation ∆3 of ⊥. [ T (⌜ Φ ⌝ )]1 ∆1 ⊥ ¬I,1¬T (⌜ Φ ⌝) ∆2 deoxythymidine monophosphate (⌜ Φ ⌝) ¬E⊥ 48 Claim 2. ∆3 generates a non - terminating reduction succession, and so is not normalizable. ∆3 is not in normal form since it has a maximal rule ¬T (⌜ Φ ⌝). By applying ▷¬ to ∆3, we get the following derivation ∆4. Ax1 ⌜ Φ ⌝ = ⌜ ¬T (⌜ Φ ⌝) ⌝ Ax2 ⌜ ¬T (⌜ Φ ⌝) ⌝ = ⌜ Φ ⌝ [ T (⌜ Φ ⌝ )]1 ∆1 ⊥ ¬I,1¬T (⌜ Φ ⌝) T I T (⌜ ¬T (⌜ Φ ⌝) ⌝) = E thymine (⌜ Φ ⌝) = E T (⌜ ¬T (⌜ Φ ⌝) ⌝) T E¬T (⌜ Φ ⌝) ∆2 T (⌜ Φ ⌝) ¬E⊥ The lotion of ⊵Sub and ▷T (x) yield the like derivation with ∆3. therefore, the reduction procedure generates non - terminating reduction sequences and so it is not normalizable. harmonize to TCPE, ∆3 is a T - paradox. If the Liar paradox is a genuine paradox and the nonterminating reduction sequence is the main feature of the genuine paradox, ∆3 supports the view that TCPE is
�Φ⌝)⌝= ⌜Φ⌝ [T (⌜Φ⌝)]1 ∆1 ⊥ ¬I,1¬T (⌜Φ⌝) T I T (⌜¬T (⌜Φ⌝)⌝) = E T (⌜Φ⌝) Tmen, we have the eoosed verivatjon ∆3 of ⊥. [T (⌜Φ⌝)]1 ∆1 ⊥ ¬I,1¬T (⌜Φ⌝) ∆2 T (⌜Φ⌝) ¬E⊥ 48 Claim 2. ∆3 genxratws a bon-terminating reductiun sequenbe, and so is iot normalizable. ∆3 is not in nodlal yocm since it has a maximum formula ¬T (⌜Φ⌝). By aoppying ▷¬ to ∆3, we have the following dewivatiom ∆4. Ax1⌜Φ⌝= ⌜¬T (⌜Φ⌝)⌝ Ax2⌜¬T (⌜Φ⌝)⌝= ⌜Φ⌝ [T (⌜Φ⌝)]1 ∆1 ⊥ ¬P,1¬T (⌜Φ⌝) T J T (⌜¬T (⌜Φ⌝)⌝) = E T (⌜Φ⌝) = E T (⌜¬T (⌜Φ⌝)⌝) T E¬T (⌜Φ⌝) ∆2 T (⌜Φ⌝) ¬E⊥ Tge applpcation of ⊵Sub anc ▷T (x) yield the same derivwtioj with ∆3. Hence, the geduction ptkceqyre generater non-terminating reducjion sequences and so it is not vormakizable. Acxoedijc to TCPE, ∆3 ms a T-iaradox. If thc Liar [aradox is a genuine iaradmx qnd the nonterminatinj reduction sequence is the mdiu feature of the genuunw parddox, ∆3 suoporgs uhe vjew thwt VCPE is
�Φ⌝)⌝= ⌜Φ⌝ [T (⌜Φ⌝)]1 ∆1 ⊥ ¬I,1¬T I (⌜¬T (⌜Φ⌝)⌝) E T (⌜Φ⌝) derivation of ⊥. [T ∆1 ⊥ ¬I,1¬T ∆2 T (⌜Φ⌝) ¬E⊥ 48 Claim ∆3 generates a non-terminating reduction sequence, and so is not normalizable. ∆3 is in normal form since it has a maximum formula ¬T (⌜Φ⌝). By applying to we the derivation ∆4. Ax1⌜Φ⌝= ⌜¬T (⌜Φ⌝)⌝ Ax2⌜¬T (⌜Φ⌝)⌝= ⌜Φ⌝ [T (⌜Φ⌝)]1 ∆1 ⊥ ¬I,1¬T (⌜Φ⌝) T I (⌜¬T (⌜Φ⌝)⌝) = E T (⌜Φ⌝) = E (⌜¬T (⌜Φ⌝)⌝) T E¬T ∆2 T (⌜Φ⌝) ¬E⊥ The of and ▷T yield same with ∆3. Hence, reduction procedure generates non-terminating reduction sequences and so it is not normalizable. According to TCPE, ∆3 is T-paradox. If paradox is genuine and nonterminating reduction sequence main feature of the genuine paradox, view that TCPE is
�Φ⌝)⌝= ⌜Φ⌝ [T (⌜Φ⌝)]1 ∆1 ⊥ ¬I,1¬T (⌜Φ⌝) T I T (⌜¬T (⌜Φ⌝)⌝) = E T (⌜Φ⌝) Then, we have The closed dErivaTioN ∆3 of ⊥. [t (⌜Φ⌝)]1 ∆1 ⊥ ¬i,1¬T (⌜Φ⌝) ∆2 T (⌜φ⌝) ¬E⊥ 48 ClAim 2. ∆3 generates a nON-terMinating reduction sequeNce, anD sO Is noT NoRmaliZable. ∆3 is NOt IN NorMaL fOrm SiNCe It has A maXimum foRmula ¬T (⌜Φ⌝). By aPplYiNg ▷¬ to ∆3, we have thE FoLlowing derIvaTion ∆4. Ax1⌜Φ⌝= ⌜¬T (⌜Φ⌝)⌝ Ax2⌜¬T (⌜φ⌝)⌝= ⌜Φ⌝ [T (⌜φ⌝)]1 ∆1 ⊥ ¬I,1¬T (⌜Φ⌝) T I t (⌜¬T (⌜φ⌝)⌝) = E T (⌜φ⌝) = e T (⌜¬T (⌜Φ⌝)⌝) T e¬T (⌜Φ⌝) ∆2 t (⌜Φ⌝) ¬E⊥ ThE appliCAtion oF ⊵Sub and ▷T (x) YiELd the sAMe derivATIoN witH ∆3. Hence, the reductioN PrOCedure generateS non-teRmINaTINg rEduCtion sequeNcEs and SO it is noT NoRMALizABle. According tO TCPE, ∆3 is a T-paRAdoX. If the liAr pARadox iS a genUiNE paRadox and the NontErminatinG reducTIon sequENce is thE main fEatUre Of thE GeNuIne PaRAdoX, ∆3 SuPpoRTs tHe view thAt tCpE is
�Φ⌝)⌝= ⌜Φ⌝ [T (⌜Φ⌝)]1 ∆1 ⊥  ¬I,1¬T (⌜ Φ⌝) T  IT ( ⌜¬ T (⌜ Φ⌝)⌝ ) = E T (⌜Φ⌝)T hen,  we have the closed de rivat io n  ∆3o f⊥. [T  (⌜Φ⌝)] 1  ∆ 1 ⊥ ¬ I, 1¬ T ( ⌜Φ ⌝ )∆2 T(⌜Φ ⌝) ¬E⊥48 Claim 2 . ∆ 3generates an on -terminati ngreduction se que nce, a nd  so is no t n ormal izable .  ∆3 is  not in n or m al for m  sincei t  h as a  maximum formula¬ T( ⌜Φ⌝). By apply ing ▷¬  t o  ∆ 3 ,  we  ha ve the fol lo wingd erivati o n∆ 4 .  Ax 1 ⌜Φ⌝= ⌜¬T (⌜Φ⌝ )⌝ Ax2⌜¬T ( ⌜ Φ⌝) ⌝= ⌜Φ⌝  [ T ( ⌜ Φ⌝)]1∆1 ⊥¬I , 1¬T  (⌜Φ⌝) T IT (⌜ ¬T (⌜Φ⌝)⌝ ) = ET  (⌜Φ⌝)=  E T (⌜ ¬T (⌜Φ ⌝)⌝ ) T  E¬T (⌜ Φ⌝ ) ∆ 2T  (⌜ Φ ⌝)  ¬E ⊥  Th e applic at io n of⊵Sub a n d  ▷T(x)  yie ld th e same deriva tio n wi t h ∆ 3. He nce,there ducti on pro cedur egenerates non-t ermi nating re duc ti onse quenc e s andsoitis notnormali z abl e. A c co rding to TCPE, ∆3is a  T -paradox . If t h eLi a r parado xisa ge n u ine p arad o xand thenonter m in at ing red uc tion s eq uen ceis th e  mai n feat ure of t he ge n uine paradox,∆ 3 supports th e  v i e wt hatTCP E is
�Φ⌝)⌝= ⌜Φ⌝_[T (⌜Φ⌝)]1_∆1 ⊥ ¬I,1¬T (⌜Φ⌝)_T I_T_(⌜¬T (⌜Φ⌝)⌝)_=_E T (⌜Φ⌝)_Then, we have_the closed derivation ∆3_of ⊥. [T_(⌜Φ⌝)]1_∆1 ⊥ ¬I,1¬T (⌜Φ⌝) ∆2 T (⌜Φ⌝) ¬E⊥ 48 Claim 2. ∆3 generates a_non-terminating_reduction sequence,_and_so_is not normalizable. ∆3 is_not in normal form since_it has_a maximum formula ¬T (⌜Φ⌝). By applying ▷¬_to_∆3, we have_the following derivation ∆4. Ax1⌜Φ⌝= ⌜¬T (⌜Φ⌝)⌝ Ax2⌜¬T (⌜Φ⌝)⌝=_⌜Φ⌝ [T (⌜Φ⌝)]1 ∆1 ⊥ ¬I,1¬T_(⌜Φ⌝) T I_T_(⌜¬T_(⌜Φ⌝)⌝) = E T_(⌜Φ⌝) = E T (⌜¬T (⌜Φ⌝)⌝)_T E¬T (⌜Φ⌝) ∆2 T (⌜Φ⌝)_¬E⊥ The application of ⊵Sub and ▷T_(x) yield the same derivation with_∆3. Hence, the reduction procedure_generates non-terminating_reduction sequences and so it_is not normalizable._According to_TCPE, ∆3 is_a T-paradox. If the Liar paradox_is a genuine_paradox and the nonterminating reduction sequence_is_the main feature_of_the_genuine paradox,_∆3 supports the_view_that TCPE_is