```    1/*
2Program describing the Mendelian rules of inheritance of the color of pea
3plants. It considers a family of two parents and a child.
4The problem is, given the alleles of the parents, predict the
5probability of the color (or of its alleles) of a pea plant.
6From
7H. Blockeel. Probabilistic logical models for mendel's experiments:
8An exercise.
9In Inductive Logic Programming (ILP 2004), Work in Progress Track, 2004.
10*/
11:- use_module(library(pita)).   12
13:- if(current_predicate(use_rendering/1)).   14:- use_rendering(c3).   15:- endif.   16
17:- pita.   18
21mother(m,s).
22father(f,s).
23% family with 3 members: m is the mother of s and f is the father of s
24
25% cg(I,C,A) means that individual I has color allele A on chromosome C
26% the color alleles are p and w and the chromosomes are 1 and 2
27% color(I,Col) means that individual I has color Col
28% Col can be purple or white
29
30cg(m,1,p).
31cg(m,2,w).
32cg(f,1,w).
33cg(f,2,p).
34% we know with certainty the alleles of the parants of s
35
36map_query cg(X,1,A):0.5 ; cg(X,1,B):0.5 :- mother(Y,X),cg(Y,1,A), cg(Y,2,B).
37% the color allele of an individual on chromosome 1 is inherited from its
38% mother. The two alleles of the mother have equal probability of being
39% transmitted
40
41map_query cg(X,2,A):0.5 ; cg(X,2,B):0.5 :- father(Y,X),cg(Y,1,A), cg(Y,2,B).
42% the color allele of an individual on chromosome 2 is inherited from its
43% father. The two alleles of the mother have equal probability of being
44% transmitted
45
46
47color(X,purple) :- cg(X,_,p).
48% if an individual has a p allele its color is purple, i.e., purple is
49% dominant
50
51color(X,white) :- cg(X,1,w), cg(X,2,w).
52% if an individual has two w alleles its color is white, i.e., white is
53% recessive
54
?- `prob(color(s,purple),Prob)`. % what is the probability that the color of s' flowers is purple? % expected result 0.75 ?- `prob(color(s,white),Prob)`. % what is the probability that the color of s' flowers is white? % expected result 0.25 ?- `prob(cg(s,1,p),Prob)`. % what is the probability that the color allele on chromosme 1 of s is p? % expected result 0.5 ?- `prob(cg(s,1,w),Prob)`. % what is the probability that the color allele on chromosme 1 of s is w? % expected result 0.5 ?- `prob(cg(s,2,p),Prob)`. % what is the probability that the color allele on chromosme 2 of s is p? % expected result 0.5 ?- `prob(cg(s,2,w),Prob)`. % what is the probability that the color allele on chromosme 2 of s is w? % expected result 0.5 ?- `prob(color(s,purple),Prob)`,`bar(Prob,C)`. % what is the probability that the color of s' flowers is purple? % expected result 0.75 ?- `prob(color(s,white),Prob)`,`bar(Prob,C)`. % what is the probability that the color of s' flowers is white? % expected result 0.25 ?- `prob(cg(s,1,p),Prob)`,`bar(Prob,C)`. % what is the probability that the color allele on chromosme 1 of s is p? % expected result 0.5 ?- `prob(cg(s,1,w),Prob)`,`bar(Prob,C)`. % what is the probability that the color allele on chromosme 1 of s is w? % expected result 0.5 ?- `prob(cg(s,2,p),Prob)`,`bar(Prob,C)`. % what is the probability that the color allele on chromosme 2 of s is p? % expected result 0.5 ?- `prob(cg(s,2,w),Prob)`,`bar(Prob,C)`. % what is the probability that the color allele on chromosme 2 of s is w? % expected result 0.5 ?- `mpe(color(s,purple),Prob,Exp)`. Prob = 0.5, Exp = [```rule(0, cg(s, 1, p), [cg(s, 1, p):0.5, cg(s, 1, w):0.5], [mother(m, s), cg(m, 1, p), cg(m, 2, w)])```].
?- `mpe(color(s,white),Prob,Exp)`. Prob = 0.25, Exp = [```rule(0, cg(s, 1, w), [cg(s, 1, p):0.5, cg(s, 1, w):0.5], [mother(m, s), cg(m, 1, p), cg(m, 2, w)])```, ```rule(1, cg(s, 2, w), [cg(s, 2, w):0.5, cg(s, 2, p):0.5], [father(f, s), cg(f, 1, w), cg(f, 2, p)])```]. */