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Sea el siguiente modelo <W, R, a> W= {w 0 ,w 1 ,w 2 } R= {<w 0 ,w 1 >, <w 0 ,w 2 >} aw 1 (p)=F aw 2 (p)=T aw 2 (q)=F aw 0 (p)=F sii vW .t. <w 0 , v> y av(p)=F, como aw 1 (p)=F⇒∃vW .t. <w 0 , v> y av(p)=F aw 0 (p)=F, aw 0 (p→q)=T sii aw 0 (p)=F ó aw 0 (p)=T aw 0 (p→q)=T, como aw 2 (p)=T y aw 2 (q)=F aw 0 (p→q)=T y aw 2 (p→q)=Faw 0 (p→q)=T y vW .t. w 0 Rv y av(p→q)=F, como aw 0 ((p→q))=F sii vW .t. w 0 Rv y av(p→q)=Faw 0 (p→q)=T y aw 0 ((p→q))=F (p→q)K ((p→q)) Sea el siguiente modelo <W, R, a> W= {w 0 ,w 1 ,w 2 } R= {<w 0 ,w 1 >, <w 0 ,w 2 >} aw 1 (p)=T aw 1 (q)=F aw 2 (p)=F aw 2 (q)=T aw 0 (◊p)=T sii vW .t. w 0 Rv y av(p)=T, aw 0 (◊q)=T sii vW .t. w 0 Rv y av(p)=T, como aw 1 (p)=V y aw 2 (q)=T ⇒∃vW .t. w 0 Rv y av(p)=T, y vW .t. w 0 Rv y av(p)=T aw 0 (◊p)=T y aw 0 (◊q)=Taw 0 (◊p&◊q)=T, además aw 1 (p&q)=F sii aw 1 (p)=F ó aw 1 (q)=F, y aw 2 (p&q)=F sii aw 2 (p)=F ó aw 2 (q)=F, como aw 1 (q)=F y aw 2 (p)=F aw 0 (◊p&◊q)=T, aw 1 (p&q)=F y aw 2 (p&q)=F, como aw 0 (◊(p&q))=F sii vW si w 0 Rv, av(p&q)=F aw 0 (◊p&◊q)=T y aw 0 (◊(p&q))=F (◊p&◊q)K (◊(p&q))

Ejemplo teorí de modelos LMP

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Ejemplos de teoría de modelos LMP

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  • SeaelsiguientemodeloW={w0,w1,w2}R={,}aw1(p)=Faw2(p)=Taw2(q)=Faw0(p)=FsiivW.t.yav(p)=F,comoaw1(p)=FvW.t.yav(p)=Faw0(p)=F,aw0(pq)=Tsiiaw0(p)=Faw0(p)=Taw0(pq)=T,comoaw2(p)=Tyaw2(q)=Faw0(pq)=Tyaw2(pq)=Faw0(pq)=TyvW.t.w0Rvyav(pq)=F,comoaw0((pq))=FsiivW.t.w0Rvyav(pq)=Faw0(pq)=Tyaw0((pq))=F(pq)K((pq))SeaelsiguientemodeloW={w0,w1,w2}R={,}aw1(p)=Taw1(q)=Faw2(p)=Faw2(q)=Taw0(p)=TsiivW.t.w0Rvyav(p)=T,aw0(q)=TsiivW.t.w0Rvyav(p)=T,comoaw1(p)=Vyaw2(q)=TvW.t.w0Rvyav(p)=T,yvW.t.w0Rvyav(p)=Taw0(p)=Tyaw0(q)=Taw0(p&q)=T,ademsaw1(p&q)=Fsiiaw1(p)=Faw1(q)=F,yaw2(p&q)=Fsiiaw2(p)=Faw2(q)=F,comoaw1(q)=Fyaw2(p)=Faw0(p&q)=T,aw1(p&q)=Fyaw2(p&q)=F,comoaw0((p&q))=FsiivWsiw0Rv,av(p&q)=Faw0(p&q)=Tyaw0((p&q))=F(p&q)K((p&q))

  • SeaelsiguientemodeloW={w0}R={}aw1(p)=Faw1(q)=Faw0(~~p)=Tsiiaw0(~p)=Fyaw0(p)=FsiivWsiw0Rv,av(p)=F,comovW.t.w0Rvyav(p)=FyvW.t.w0Rvyav(p)=TvW.t.w0Rvyav(~p)=TyvW.t.w0Rvyav(p)=T,vWsiw0Rv,av(~p)=FyvWsiw0Rv,av(p)=F,dadoqueaw0(~p)=FsiivWsiw0Rv,av(~p)=Faw0(~p)=Fyaw0(p)=Faw0(~~p)=Tyaw0(p)=F(~~p)K(p)

  • SeaelsiguientemodeloW={w0,w1,w2,w3,w4,w5}R={,,,}aw1(q)=Faw2(q)=Faw4(s)=Faw3(r)=Taw4(r)=Taw0(~(q~r))=Tsiiaw0((q~r))=F,yaw0((~q&s))=TsiivW.t.w0Rvyav((~q&s))=T,comoaw0((q~r))=FsiivWsiw0Rv,av(q~r)=Faw0(~(q~r))=TsiivWsiw0Rv,av(q~r)=F,yaw0((~q&s))=TsiivW.t.w0Rvyav((~q&s))=T,ademsaw3((~q&s))=TsiivWsiw3Rv,av(~q&s)=T,comovW.t.w3Rvyav(~q&s)=FporloquevWsiw3Rv,av(~q&s)=Taw0(~(q~r))=TsiivWsiw0Rv,av(q~r)=F,yaw0((~q&s))=TsiivW.t.w0Rvyav((~q&s))=T,ademsaw3((~q&s))=Tyaw1((~q&s))=TsiivWsiw1Rv,av((~q&s))=Tcomoaw3((~q&s))=T,entoncesvWsiw1Rv,av((~q&s))=Taw0(~(q~r))=TsiivWsiw0Rv,av(q~r)=F,yaw0((~q&s))=TsiivW.t.w0Rvyav((~q&s))=T,tambinaw0((~q&s))=T,porloquevW.t.w0Rvyav((~q&s))=Taw0(~(q~r))=TsiivWsiw0Rv,av(q~r)=F,yaw0((~q&s))=T,tenemostambinqueaw1(~r)=FsiivW.t.w1Rvyav(~r)=Fyaw2(~r)=FsiivW.t.w2Rvyav(~r)=F,comoaw3(r)=Tyaw4(r)=T,entoncesaw3(~r)=Fyaw4(~r)=F,porloquevW.t.w1Rvyav(~r)=FyvW.t.w2Rvyav(~r)=Faw0(~(q~r))=TsiivWsiw0Rv,av(q~r)=F,yaw0((~q&s))=T,ademsaw1(~r)=Fyaw2(~r)=F,comoaw1(q)=Fydadoqueaw1(q~r)=Fsiiaw1(q)=Fyaw1(~r)=Faw0(~(q~r))=TsiivWsiw0Rv,av(q~r)=F,yaw0((~q&s))=T,ademsaw1(q~r)=Fyaw2(~r)=F,comoaw2(q)=Fydadoqueaw2(q~r)=Fsiiaw1(q)=Fyaw1(~r)=Faw0(~(q~r))=TsiivWsiw0Rv,av(q~r)=F,yaw0((~q&s))=T,ademsaw1(q~r)=Fyaw2(q~r)=F,porloquevWsiw0Rv,av(q~r)=Faw0(~(q~r))=Tyaw0((~q&s))=T,ademsaw0((r(~q&s)))=FsiivW.t.w0Rvyav((r(~q&s)))=Fyaw2((r(~q&s)))=FsiivWsiw2Rv,av(r(~q&s))=F,tambintenemosqueaw4(r(~q&s))=Fsiiaw4(r)=Tyaw4(~q&s)=F.Asuvezaw4(~q&s)=Fsiiaw4(~q)=Faw4(s)=F,comoaw4(s)=Faw0(~(q~r))=Tyaw0((~q&s))=T,ademsaw0((r(~q&s)))=FsiivW.t.w0Rvyav((r(~q&s)))=Fyaw2((r(~q&s)))=FsiivWsiw2Rv,av(r(~q&s))=F,tambintenemosqueaw4(r(~q&s))=F,porloquevWsiw2Rv,av(r(~q&s))=F

  • aw0(~(q~r))=Tyaw0((~q&s))=T,ademsaw0((r(~q&s)))=FsiivW.t.w0Rvyav((r(~q&s)))=Fyaw2((r(~q&s)))=F,siendoasvW.t.w0Rvyav((r(~q&s)))=Faw0(~(q~r))=T,aw0((~q&s))=Tyaw0((r(~q&s)))=F~(q~r),(~q&s)K(r(~q&s))SeaelsiguientemodeloW={w0,w1,w2}R={,}aw2(p)=Faw2(q)=FComoaw2(p)=F,vW.t.w1Rvyav(p)=Fydadoqueaw2(q)=F,entoncesvWsiw1Rv,av(q)=Faw2(p)=Fyaw2(q)=Faw2(~p)=vyaw2(~p)=Faw2(q)=Faw2(~p)=vyaw2(~p&q)=Faw2(~p(~p&q))=F,siendoasvW.t.w0Rvyav(~p(~p&q))=Faw0((~p(~p&q)))=FK(~p(~p&q))SeaelsiguientemodeloW={w0,w1,w2}R={,}aw1(p)=TComovW.t.w2Rvyav(p)=TyvW.t.w2Rvyav(p)=TvWsiw2Rv,av(p)=FyvWsiw2Rv,av(p)=Faw2(p)=Fyaw2(q)=Faw2(pq)=FvW.t.w0Rvyav((pq))=Faw0((pq))=F,dadoqueaw1(p)=T,entoncesvW.t.w0Rvyav(p)=Taw0(p)=Tyaw0((pq))=FpK(pq)SeaelsiguientemodeloW={w0,w1}R={,}aw1(p)=Faw1(q)=T

  • Comoaw1(p)=Fyaw1(q)=T,vWsiw0Rv,av(q)=TyvW.t.w0Rvyav(q)=Taw0(q)=Tyaw0(q)=T,aw1(p)=Faw0(q)=Tyaw0(p)=Taw0(q)=T,aw1(p)=Faw0(q)=T,aw0(pq)=Tyaw1(p)=Faw0(q)=T,aw0(pq)=Tyaw1(p)=Faw1(q)=Faw0(q)=T,aw0(pq)=Tyaw1(pq)=Faw0(q)=T,aw0(pq)=TyvW.t.w0Rvyav(pq)=Faw0(q)=T,aw0(pq)=Tyaw0((pq))=Fq,(pq)K0(pq)