Stochastic Logic Programs¶

% a stochastic logic program defining a distribution over simple sentences with number agreement % recall that in SLPs, the probabilities of all rules with the same head predicate sum to one and define a mutually exclusive choice on how to continue a proof % furthermore, repeated choices are independent, i.e., no stochastic memoization % % 1.0 : s(List) :- % s(List,[]). % % 1.0 : s(List,Rest) :- % np(List,Mid,Number), % vp(Mid,Rest,Number). % % 0.4 : np(List,Rest,sing) :- % det(List,Mid,sing), % n(Mid,Rest,sing). % 0.4 : np(List,Rest,pl) :- % n(List,Rest,pl). % 0.2 : np(List,Rest,pl) :- % det(List,Mid,pl), % n(Mid,Rest,pl). % % 1.0 : vp(List,Rest,Num) :- % v(List,Mid,Num), % np(Mid,Rest,_). % % 1/3 : det([the|L],L,pl). % 1/3 : det([the|L],L,sing). % 1/3 : det([a|L],L,sing). % % 0.25 : n([cat|L],L,sing). % 0.15 : n([mouse|L],L,sing). % 0.1 : n([dog|L],L,sing). % 0.25 : n([cats|L],L,pl). % 0.15 : n([mice|L],L,pl). % 0.1 : n([dogs|L],L,pl). % % 0.35 : v([chases|L],L,sing). % 0.15 : v([sees|L],L,sing). % 0.2 : v([chase|L],L,pl). % 0.3 : v([see|L],L,pl). % use counter-based trial IDs for each head predicate with a stochastic choice, and explicit split rather than difference lists % s(Num) -> np(Num),vp(Num) s(W,Num,np(N,NN),det(D,DD),n(M,MM),v(V,VV)) :- split(W,W1,W2), np(W1,Num,np(N,NI),det(D,DI),n(M,MI),v(V,VI)), vp(W2,Num,np(NI,NN),det(DI,DD),n(MI,MM),v(VI,VV)). % np(Num) -> 0.4:: det(sg),n(sg) | 0.4:: n(pl) | 0.2::det(pl),n(pl) 0.4::np_to(N,sg_dn); 0.4::np_to(N,pl_n); 0.2::np_to(N,pl_dn). np(W,sg,np(N,NN),det(D,DD),n(M,MM),v(V,VV)) :- np_to(N,sg_dn), NI is N+1, split(W,W1,W2), det(W1,sg,np(NI,N1),det(D,D1),n(M,M1),v(V,V1)), n(W2,sg,np(N1,NN),det(D1,DD),n(M1,MM),v(V1,VV)). np(W,pl,np(N,NN),det(D,DD),n(M,MM),v(V,VV)) :- np_to(N,pl_n), NI is N+1, n(W,pl,np(NI,NN),det(D,DD),n(M,MM),v(V,VV)). np(W,pl,np(N,NN),det(D,DD),n(M,MM),v(V,VV)) :- np_to(N,pl_dn), NI is N+1, split(W,W1,W2), det(W1,pl,np(NI,N1),det(D,D1),n(M,M1),v(V,V1)), n(W2,pl,np(N1,NN),det(D1,DD),n(M1,MM),v(V1,VV)). % vp(Num) -> v(Num), np(_) vp(W,Num,np(N,NN),det(D,DD),n(M,MM),v(V,VV)) :- split(W,W1,W2), v(W1,Num,np(N,NI),det(D,DI),n(M,MI),v(V,VI)), np(W2,_,np(NI,NN),det(DI,DD),n(MI,MM),v(VI,VV)). % det(Num) -> 1/3 the(pl) | 1/3 the(sg) | 1/3 a(sg) 1/3::det_to(N,the_pl); 1/3::det_to(N,the_sg); 1/3::det_to(N,a_sg). det([the],pl,np(N,N),det(D,DD),n(M,M),v(V,V)) :- det_to(D,the_pl), DD is D+1. det([the],sg,np(N,N),det(D,DD),n(M,M),v(V,V)) :- det_to(D,the_sg), DD is D+1. det([a],sg,np(N,N),det(D,DD),n(M,M),v(V,V)) :- det_to(D,a_sg), DD is D+1. % n(Num) -> 0.25 cat(sg) | 0.15 mouse(sg) | 0.1 dog(sg) | 0.25 cats(pl) | 0.15 mice(pl) | 0.1 dogs(pl) 0.25::n_to(N,cat_sg); 0.15::n_to(N, mouse_sg) ; 0.1::n_to(N, dog_sg) ; 0.25::n_to(N, cats_pl) ; 0.15::n_to(N, mice_pl) ; 0.1::n_to(N, dogs_pl). n([cat],sg,np(N,N),det(D,D),n(M,MM),v(V,V)) :- n_to(M,cat_sg), MM is M+1. n([mouse],sg,np(N,N),det(D,D),n(M,MM),v(V,V)) :- n_to(M,mouse_sg), MM is M+1. n([dog],sg,np(N,N),det(D,D),n(M,MM),v(V,V)) :- n_to(M,dog_sg), MM is M+1. n([cats],pl,np(N,N),det(D,D),n(M,MM),v(V,V)) :- n_to(M,cats_pl), MM is M+1. n([mice],pl,np(N,N),det(D,D),n(M,MM),v(V,V)) :- n_to(M,mice_pl), MM is M+1. n([dogs],pl,np(N,N),det(D,D),n(M,MM),v(V,V)) :- n_to(M,dogs_pl), MM is M+1. % v(Num) -> 0.35 chases(sg) | 0.15 sees(sg) | 0.2 chase(pl) | 0.3 see(pl) 0.35::v_to(N, chases_sg) ; 0.15::v_to(N, sees_sg) ; 0.2::v_to(N, chase_pl) ; 0.3::v_to(N, see_pl). v([chases],sg,np(N,N),det(D,D),n(M,M),v(V,VV)) :- v_to(V,chases_sg), VV is V+1. v([sees],sg,np(N,N),det(D,D),n(M,M),v(V,VV)) :- v_to(V,sees_sg), VV is V+1. v([chase],pl,np(N,N),det(D,D),n(M,M),v(V,VV)) :- v_to(V,chase_pl), VV is V+1. v([see],pl,np(N,N),det(D,D),n(M,M),v(V,VV)) :- v_to(V,see_pl), VV is V+1. % initialize all counters to 0, and leave number open word(L) :- s(L,_Num,np(0,_),det(0,_),n(0,_),v(0,_)). % split(+T,-P,-S) splits the list T into two non-empty sublists P(refix) and S(uffix) % note that T needs to have fixed length for this to terminate split([A,B|C],[A],[B|C]). split([A,B|C],[A|D],E) :- split([B|C],D,E). % compute posteriors of correct sentences (or sample a correct sentence) % we need to fix the length of the list to ensure split/3 has a finite number of solutions query(word([_,_,_,_,_])). query(word([_,_,_,_])). query(word([_,_,_])). evidence(is_word). % this grammar can only produce words of length 3/4/5 % the probability of getting a word is 0.067222 is_word :- word([_,_,_]). is_word :- word([_,_,_,_]). is_word :- word([_,_,_,_,_]).