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chapter9.pl
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% Prolog programs from Chapter 9 of the book %
% SIMPLY LOGICAL: Intelligent reasoning by example %
% (c) Peter A. Flach/John Wiley & Sons, 1994. %
% %
% Predicates: induce/2,3 %
% theta_subsumes/2 %
% anti_unify/3 %
% theta_lgg/3 %
% %
% NB. This file needs predicates defined in %
% the file 'library'. %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
:-consult(library).
%% Naive induction %%
%% NB. The inductive meta-interpreter uses cl/2 rather than clause/2
%% in order to avoid problems with built-in predicate not/1
induce(E,H):-
induce(E,[],H).
% induce(E,H0,H) <- H is inductive explanation of E
induce(true,H,H).
induce((A,B),H0,H):-
induce(A,H0,H1),
induce(B,H1,H).
induce(A,H0,H):-
cl(A,B),
induce(B,H0,H).
induce(A,H0,H):- % already assumed
element((A:-B),H0),
induce(B,H0,H). % proceed with body of rule
induce(A,H0,[(A:-B)|H]):- % A:-B can be added to the explanation
inducible((A:-B)), % if it's inducible
not element((A:-B),H0), % and if it's not already there
induce(B,H0,H). % proceed with body of rule
inducible((flies(X):-bird(X),has_feathers(X),has_beak(X))).
inducible((flies(X):-bird(X),has_feathers(X))).
inducible((flies(X):-bird(X),has_beak(X))).
inducible((flies(X):-has_feathers(X),has_beak(X))).
inducible((flies(X):-bird(X))).
inducible((flies(X):-has_feathers(X))).
inducible((flies(X):-has_beak(X))).
inducible((flies(X):-true)).
cl(bird(tweety),true).
cl(has_feathers(tweety),true).
cl(bird(polly),true).
cl(has_beak(polly),true).
% ?-induce(flies(tweety),H).
% ?-induce(flies(polly),H).
%%% 9.1 Generalisation and specialisation %%%
theta_subsumes((H1:-B1),(H2:-B2)):-
not((H1=H2,ground(B2),
not subset(B1,B2))).
ground(Term):-
numbervars(Term,0,N).
:-op(600,xfx,'<-').
anti_unify(Term1,Term2,Term):-
anti_unify(Term1,Term2,Term,[],S1,[],S2).
anti_unify(Term1,Term2,Term1,S1,S1,S2,S2):-
Term1 == Term2,!.
anti_unify(Term1,Term2,V,S1,S1,S2,S2):-
subs_lookup(S1,S2,Term1,Term2,V),!.
anti_unify(Term1,Term2,Term,S10,S1,S20,S2):-
nonvar(Term1),nonvar(Term2),
functor(Term1,F,N),functor(Term2,F,N),!,
functor(Term,F,N),
anti_unify_args(N,Term1,Term2,Term,S10,S1,S20,S2).
anti_unify(Term1,Term2,V,S10,[Term1<-V|S10],S20,[Term2<-V|S20]).
anti_unify_args(0,Term1,Term2,Term,S1,S1,S2,S2).
anti_unify_args(N,Term1,Term2,Term,S10,S1,S20,S2):-
N>0,N1 is N-1,
arg(N,Term1,Arg1),
arg(N,Term2,Arg2),
arg(N,Term,Arg),
anti_unify(Arg1,Arg2,Arg,S10,S11,S20,S21),
anti_unify_args(N1,Term1,Term2,Term,S11,S1,S21,S2).
subs_lookup([T1<-V|Subs1],[T2<-V|Subs2],Term1,Term2,V):-
T1 == Term1,
T2 == Term2,!.
subs_lookup([S1|Subs1],[S2|Subs2],Term1,Term2,V):-
subs_lookup(Subs1,Subs2,Term1,Term2,V).
% ?-anti_unify(2*2=2+2,3*2=3+3,T,[],S1,[],S2).
% T = X*2=X+X
% S1 = [2<-X]
% S2 = [3<-X]
theta_lgg((H1:-B1),(H2:-B2),(H:-B)):-
anti_unify(H1,H2,H,[],S10,[],S20),
theta_lgg_bodies(B1,B2,[],B,S10,S1,S20,S2).
theta_lgg_bodies([],B2,B,B,S1,S1,S2,S2).
theta_lgg_bodies([L|B1],B2,B0,B,S10,S1,S20,S2):-
theta_lgg_literal(L,B2,B0,B00,S10,S11,S20,S21),
theta_lgg_bodies(B1,B2,B00,B,S11,S1,S21,S2).
theta_lgg_literal(L1,[],B,B,S1,S1,S2,S2).
theta_lgg_literal(L1,[L2|B2],B0,B,S10,S1,S20,S2):-
same_predicate(L1,L2),
anti_unify(L1,L2,L,S10,S11,S20,S21),
theta_lgg_literal(L1,B2,[L|B0],B,S11,S1,S21,S2).
theta_lgg_literal(L1,[L2|B2],B0,B,S10,S1,S20,S2):-
not same_predicate(L1,L2),
theta_lgg_literal(L1,B2,B0,B,S10,S1,S20,S2).
%%% same_predicate/2: see file 'library'
% theta_lgg((element(c,[b,c]):-[element(c,[c])]),
% (element(d,[b,c,d]):-[element(d,[c,d]),element(d,[d])]),
% C).
% C = element(X,[b,c|Y]):-[element(X,[X]),element(X,[c|Y])]