2009-03-09 00:40:50 +00:00
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% ProbLog program describing a probabilistic graph
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% (running example from ProbLog presentations)
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2009-03-16 15:13:47 +00:00
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:- use_module(library(problog)).
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2009-03-09 00:40:50 +00:00
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%%%%
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% background knowledge
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%%%%
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% definition of acyclic path using list of visited nodes
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path(X,Y) :- path(X,Y,[X],_).
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path(X,X,A,A).
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path(X,Y,A,R) :-
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X\==Y,
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edge(X,Z),
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absent(Z,A),
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path(Z,Y,[Z|A],R).
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% using directed edges in both directions
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edge(X,Y) :- dir_edge(Y,X).
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edge(X,Y) :- dir_edge(X,Y).
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% checking whether node hasn't been visited before
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absent(_,[]).
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absent(X,[Y|Z]):-X \= Y, absent(X,Z).
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%%%%
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% probabilistic facts
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%%%%
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0.9::dir_edge(1,2).
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0.8::dir_edge(2,3).
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0.6::dir_edge(3,4).
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0.7::dir_edge(1,6).
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0.5::dir_edge(2,6).
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0.4::dir_edge(6,5).
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0.7::dir_edge(5,3).
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0.2::dir_edge(5,4).
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% example queries about path(1,4)
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%
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%%% explanation probability (and facts involved)
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% ?- problog_max(path(1,4),Prob,FactsUsed).
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% FactsUsed = [dir_edge(1,2),dir_edge(2,3),dir_edge(3,4)],
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% Prob = 0.432 ?
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% yes
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%%% success probability
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% ?- problog_exact(path(1,4),Prob,Status).
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% 8 proofs
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% Prob = 0.53864,
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% Status = ok ?
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% yes
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%%% lower bound using 4 best proofs
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% ?- problog_kbest(path(1,4),4,Prob,Status).
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% 4 proofs
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% Prob = 0.517344,
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% Status = ok ?
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% yes
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%%% approximation using monte carlo, to reach 95%-confidence interval width 0.01
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% ?- problog_montecarlo(path(1,4),0.01,Prob).
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% Prob = 0.537525 ?
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% yes
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%%% upper and lower bound using iterative deepening, final interval width 0.01
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% ?- problog_delta(path(1,4),0.01,Bound_low,Bound_up,Status).
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% Bound_low = 0.5354096,
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% Bound_up = 0.53864,
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% Status = ok ?
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% yes
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%%% upper and lower bound obtained cutting the sld tree at probability 0.1 for each branch
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% ?- problog_threshold(path(1,4),0.1,Bound_low,Bound_up,Status).
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% 4 proofs
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% Bound_low = 0.517344,
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% Bound_up = 0.563728,
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% Status = ok ?
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% yes
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%%% lower bound obtained cutting the sld tree at probability 0.2 for each branch
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% ?- problog_low(path(1,4),0.2,Bound_low,Status).
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% 1 proofs
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% Bound_low = 0.432,
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% Status = ok ?
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% yes
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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