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Christian Ohlsson
2026-03-05 13:42:07 +01:00
commit e309cbad69
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/*****************************/
/* Christian Ohlsson */
/* Logik för dataloger */
/* Karlstad 990228 */
/* Laboration 3 i Logik */
/*****************************/
/* Functions included */
/* prenex */
/* implout */
/* negin */
/* kvant */
/* free_in */
/* rename_var */
/*****************************/
:- op(200,fx,~).
:- op(400,xfy,#).
:- op(400,xfy,&).
:- op(700,xfy,->).
:- op(700,xfy,<->).
prenex(Formel,PNF):-
implout(Formel,Svar1),
negin(Svar1,Svar2),
kvant(Svar2,PNF,[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10],L).
/* ***************************** IMPLOUT **************************** */
implout((P<->Q),((P1&Q1)#(~P1&~Q1))) :- !,implout(P,P1),implout(Q,Q1).
implout((P->Q),(~P1#Q1)) :- !,implout(P,P1),implout(Q,Q1).
implout(all(X,P),all(X,P1)) :- !,implout(P,P1).
implout(exist(X,P),exist(X,P1)) :- !,implout(P,P1).
implout((P&Q),(P1&Q1)) :- !,implout(P,P1),implout(Q,Q1).
implout((P#Q),(P1#Q1)) :- !,implout(P,P1),implout(Q,Q1).
implout((~P),(~P1)) :- !,implout(P,P1).
implout(P,P).
/* ***************************** NEGIN **************************** */
negin((~P),P1) :- !,neg(P,P1).
negin(all(X,P),all(X,P1)) :- !,negin(P,P1).
negin(exist(X,P),exist(X,P1)) :- !,negin(P,P1).
negin((P&Q),(P1&Q1)) :- !,negin(P,P1),negin(Q,Q1).
negin((P#Q),(P1#Q1)) :- !,negin(P,P1),negin(Q,Q1).
negin(P,P).
neg((~P),P1) :- !,negin(P,P1).
neg(all(X,P),exist(X,P1)) :- !,neg(P,P1).
neg(exist(X,P),all(X,P1)) :- !,neg(P,P1).
neg((P&Q),(P1#Q1)) :- !,neg(P,P1),neg(Q,Q1).
neg((P#Q),(P1&Q1)) :- !,neg(P,P1),neg(Q,Q1).
neg(P,(~P)).
/* ***************************** RENAME-VAR **************************** */
r_v(X,exist(X,P),exist(F,P1),[F|R]):- r_v(X,P,P1,[F|R]).
r_v(X,exist(Y,P),exist(Y,P1),[F|R]):- X\==Y, r_v(X,P,P1,[F|R]).
r_v(X,all(X,P),all(F,P1),[F|R]):- r_v(X,P,P1,[F|R]).
r_v(X,all(Y,P),all(Y,P1),[F|R]):- X\==Y, r_v(X,P,P1,[F|R]).
r_v(X,Y#Z,Y1#Z1,[F|R]):- r_v(X,Y,Y1,[F|R]),r_v(X,Z,Z1,[F|R]).
r_v(X,Y&Z,Y1&Z1,[F|R]):- r_v(X,Y,Y1,[F|R]),r_v(X,Z,Z1,[F|R]).
r_v(X,Y->Z,Y1->Z1,[F|R]):- r_v(X,Y,Y1,[F|R]),r_v(X,Z,Z1,[F|R]).
r_v(X,Y<->Z,Y1<->Z1,[F|R]):- r_v(X,Y,Y1,[F|R]),r_v(X,Z,Z1,[F|R]).
r_v(X,Y,Y2,[F|R]):- Y=..[T,S],r_v(X,S,Y1,[F|R]), Y2=..[T,Y1].
r_v(X,[T|S],[F|S1],[F|R]):- X==T, r_v(X,S,S1,[F|R]).
r_v(X,[T|S],[S2|S1],[F|R]):- X\==T, r_v(X,S,S1,[F|R]),r_v(X,T,S2,[F|R]).
r_v(X,~P,~P1,[F|R]):- r_v(X,P,P1,[F|R]).
r_v(X,X,F,[F|R]).
r_v(X,U,U,[F|R]):- X\==U.
/* ***************************** FREE ****************************** */
free_in(X,exist(Y,P)):- X\==Y, free_in(X,P).
free_in(X,all(Y,P)):- X\==Y, free_in(X,P).
free_in(X,Y#Z):-free_in(X,Y);free_in(X,Z).
free_in(X,Y&Z):-free_in(X,Y);free_in(X,Z).
free_in(X,Y->Z):-free_in(X,Y);free_in(X,Z).
free_in(X,Y<->Z):-free_in(X,Y);free_in(X,Z).
free_in(X,Y):- Y=..[F,R],free_in(X,R).
free_in(X,[F|R]):-free_in(X,F);free_in(X,R).
free_in(X,~Z):-free_in(X,Z).
free_in(X,X).
/* ********************************************************************* */
/* ***************************** ALL & ***************************** */
kvant(all(X,Y)&Z,SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(all(X,(Y1&Z2)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(all(X,(Y1&Z2)),SY,L2,L3)).
/* ***************************** & ALL **************************** */
kvant(Z&all(X,Y),SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(all(X,(Z2&Y1)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(all(X,(Z2&Y1)),SY,L2,L3)).
/* ***************************** ALL # **************************** */
kvant(all(X,Y)#Z,SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(all(X,(Y1#Z2)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(all(X,(Y1#Z2)),SY,L2,L3)).
/* ***************************** # ALL **************************** */
kvant(Z#all(X,Y),SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(all(X,(Z2#Y1)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(all(X,(Z2#Y1)),SY,L2,L3)).
/* *************************** EXIST & ************************** */
kvant(exist(X,Y)&Z,SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(exist(X,(Y1&Z2)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(exist(X,(Y1&Z2)),SY,L2,L3)).
/* *************************** & EXIST ************************** */
kvant(Z&exist(X,Y),SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(exist(X,(Z2&Y1)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(exist(X,(Z2&Y1)),SY,L2,L3)).
/* *************************** EXIST # ************************** */
kvant(exist(X,Y)#Z,SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(exist(X,(Y1#Z2)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(exist(X,(Y1#Z2)),SY,L2,L3)).
/* *************************** # EXIST ************************** */
kvant(Z#exist(X,Y),SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(exist(X,(Z2#Y1)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(exist(X,(Z2#Y1)),SY,L2,L3)).
/* *************************** & ************************** */
kvant(P&Q,PQ,L,L3):-
kvant(P,P1,L,L1),
kvant(Q,Q1,L1,L2),
((P1\==P);(Q1\==Q)),
kvant(P1&Q1,PQ,L2,L3).
/* *************************** # ************************** */
kvant(P#Q,PQ,L,L3):-
kvant(P,P1,L,L1),
kvant(Q,Q1,L1,L2),
((P1\==P);(Q1\==Q)),
kvant(P1#Q1,PQ,L2,L3).
/* *************************** EXIST ************************** */
kvant(all(X,F),all(X,F1),L1,L2):-
kvant(F,F1,L1,L2).
/* *************************** ALL ************************** */
kvant(exist(X,F),exist(X,F1),L1,L2):-
kvant(F,F1,L1,L2).
/* *************************** BASFALL ************************** */
kvant(X,X,L,L).