An interpreter for belief networks.

Source: PROLOG programming for artificial intelligence, 3rd Edition, Harlow, 2001, ISBN 0-201-40375-7.

Program source code: belief_networks.pl

% Figure 15.11  An interpreter for belief networks.
 
:- op( 900, fy, not).
 
% not Goal): negation as failure; 
%   Note: This is often available as a built-in predicate,
%   often written as prefix operator "\+", e.g. \+ likes(mary,snakes)
 
not Goal  :-
  Goal, !, fail
  ; 
  true.
 
% Reasoning in belief networks
 
% Belief network is represented by relations:
%    parent( ParentNode, Node)
%    p( Node, ParentStates, Prob)
%      where Prob is conditional probability of Node given 
%      values of parent variables ParentStates, for example: 
%      p( alarm, [ burglary, not earthquake], 0.99)
%    p( Node, Prob)
%      probability of node without parents
 
 
% prob( Event, Condition, P):
%   probability of Event, given Cond, is P;
%   Event is a variable, its negation, or a list
%   of simple events representing their conjunction
 
prob( [X | Xs], Cond, P)  :-  !,   % Probability of conjunction
  prob( X, Cond, Px),
  prob( Xs, [X | Cond], PRest),
  P is Px * PRest.
 
prob( [], _, 1)  :-  !.            % Empty conjunction
 
prob( X, Cond, 1)  :-
  member( X, Cond), !.             % Cond implies X
 
prob( X, Cond, 0)  :-
  member( not X, Cond), !.         % Cond implies X is false
 
prob( not X, Cond, P)  :-  !,      % Probability of negation
  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 involve 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),  % Conditions on parents
  sum_probs( CPlist, Cond, P).
 
% sum_probs( CondsProbs, Cond, WeigthedSum)
%   CondsProbs is a list of conditions and corresponding probabilities,
%   WeightedSum is weighted sum of probabilities of Conds given Cond
 
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, not 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).