reasoning in belief network with prolog - prolog

Question

I have a problem in Prolog for my final project. I try to reason about train system disruption pattern using bayesian network and prolog. I have bayesian network looks like following figure :
Bayesian Network Picture
I read on books Prolog Programming for Articial Intellegent 3rd addtion by Ivan Bratko, and I found how to represent Bayesian Network in Prolog.
You can see the Prolog code as follow :
%here is the rule for reasoning in bayesian network from the book :
prob([X|Xs],Cond,P) :- !,
prob(X, Cond, Px),
prob(Xs, [X|Cond], PRest),
P is Px * PRest.
prob([],_,1):- !.
prob(X, Cond, 1) :-
member(X, Cond),!.
prob(X, Cond, 0) :-
member(\+ X, Cond), !.
prob(\+ X, Cond, P) :- !,
prob(X, Cond, P0),
P is 1-P0.
%Use Bayes rule if condition involves a descendant of X
prob(X, Cond0, P):-
delete(Y, Cond0, Cond),
predecessor(X,Y),!, %Y is a descendant of X
prob(X, Cond, Px),
prob(Y, [X|Cond], PyGivenX),
prob(Y, Cond, Py),
P is Px * PyGivenX / Py. %Assuming Py > 0
%Cases when condition does not involves a descendant
prob(X, Cond, P) :-
p(X, P),!. % X a root cause - its probability given
prob(X, Cond, P) :- !,
findall((CONDi, Pi), p(X,CONDi,Pi), CPlist), %Condition on parents
sum_probs(CPlist, Cond, P).
sum_probs([],_,0).
sum_probs([(COND1,P1) | CondsProbs], COND, P) :-
prob(COND1, COND, PC1),
sum_probs(CondsProbs, COND, PRest),
P is P1 * PC1 + PRest.
predecessor(X, \+ Y) :- !, %Negated variable Y
predecessor(X,Y).
predecessor(X,Y) :-
parent(X,Y).
predecessor(X,Z) :-
parent(X,Y),
predecessor(Y,Z).
member(X, [X|_]).
member(X, [_|L]) :-
member(X,L).
delete(X, [X|L], L).
delete(X, [Y|L], [Y|L2]) :-
delete(X, L, L2).
Here also some the implementation of the bayesian network information in prolog (I only add some of them because it was too long):
p(static_inverter, [overhead_line], 0.005050505).
p(static_inverter, [\+ overhead_line], 0.000213767).
p(ac, [static_inverter], 0.5).
p(ac, [\+ static_inverter], 0.029749692).
p(door, [compressor], 0.026315789).
p(door, [\+ compressor], 0.006821).
p(horn, [compressor], 0.026315789).
p(horn, [\+ compressor], 0.000206697).
p(brake, [compressor], 0.026315789).
p(brake, [\+ compressor], 0.004340637).
p(switch, [signal, service_table], 0.5).
p(switch, [\+ signal, service_table], 0.346153846).
p(switch, [signal, \+ service_table], 0.054098361).
p(switch, [\+ signal, \+ service_table], 0.041364933).
p(overhead_line, [fire, fallen_tree], 0.5).
p(overhead_line, [fire, \+ fallen_tree], 0.005882353).
p(overhead_line, [\+ fire, fallen_tree], 0.304878049).
p(overhead_line, [\+ fire, \+ fallen_tree], 0.038850284).
p(pantograph, [overhead_line, fallen_tree], 0.038461538).
p(pantograph, [overhead_line, \+ fallen_tree], 0.002702703).
p(pantograph, [\+ overhead_line, fallen_tree], 0.017241379).
p(pantograph, [\+ overhead_line, \+ fallen_tree], 0.00440955).
for the full code you may see on here
unfortunately I have a problem when I try to reason some probabilities like :
?- prob(series, [horn], P).
?- prob(series, [brake], P).
?- prob(pantograph, [overhead_line], P).
It was said the error is something like this :
ERROR: Arithmetic: evaluation error: `zero_divisor'
ERROR: In:
ERROR: [27] _43124 is 0.045454539961694*0/0
ERROR: [25] prob([compressor],[\+brake,traction|...],_43166) at d:/kuliah/tugas/semester 8/for ta/[2] ta program/reasoningtraindisruptionwithprolog/rules.pl:2
ERROR: [24] sum_probs([(...,0.026315789),...],[\+brake,traction|...],_43216) at d:/kuliah/tugas/semester 8/for ta/[2] ta program/reasoningtraindisruptionwithprolog/rules.pl:37
ERROR: [22] prob([horn,door|...],[\+brake,traction|...],_43278) at d:/kuliah/tugas/semester 8/for ta/[2] ta program/reasoningtraindisruptionwithprolog/rules.pl:2
ERROR: [21] prob([\+brake,horn|...],[traction,wiper|...],_43334) at d:/kuliah/tugas/semester 8/for ta/[2] ta program/reasoningtraindisruptionwithprolog/rules.pl:3
ERROR: [20] prob([traction,...|...],[wiper,speedometer|...],_43390) at d:/kuliah/tugas/semester 8/for ta/[2] ta program/reasoningtraindisruptionwithprolog/rules.pl:3
Any one can help me to fix this error? Thanks in advance.

Answer 1

After introducing the safety test,
...
prob(Y, Cond, Py),
Py > 0,
P is Px * PyGivenX / Py. %Assuming Py > 0
and corrected a typo and several singleton warnings in your github code, I have these results:
?- prob(series, [horn], P).
false.
?- prob(series, [brake], P).
P = 0.086661842800551.
?- prob(pantograph, [overhead_line], P).
false.
So you can now try to understand why the code yields false instead of P = 0.0...

Answer 2

I realize why the intrpreter derive answer with zero_divisor error, it because when I query with :
?- prob(series, [horn], P).
?- prob(series, [brake], P).
?- prob(pantograph, [overhead_line], P)
All of them processed with rule :
prob(X, Cond0, P):-
delete(Y, Cond0, Cond),
predecessor(X,Y),!, %Y is a descendant of X
prob(X, Cond, Px),
prob(Y, [X|Cond], PyGivenX),
prob(Y, Cond, Py),
P is Px * PyGivenX / Py. %Assuming Py > 0
Whereas they should be processed with rule underneath :
prob(X, Cond, P) :-
p(X, P),!. % X a root cause - its probability given
prob(X, Cond, P) :- !,
findall((CONDi, Pi), p(X,CONDi,Pi), CPlist), %Condition on parents
sum_probs(CPlist, Cond, P).
Because the query not involves descendant of X
Any idea to distinguish both rules? Because I still use both rules recursively later?
I already try adding condition parent(X, Cond0) in prob(X, Cond0, P), but when I query with condition involves a descendant of X, the answer is wrong