Nested Number Guessing

This is a ProbLog variant of the nested number guessing example on http://forestdb.org/models/nested-guessing.html, illustrating nested queries using ProbLog’s subquery primitive. Two players a and b each randomly choose a number between 0 and 9, and they win if the numbers sum to 13. Player b observes a’s number before choosing, wrongly believes they win with any sum greater than 8, and conditions his choice on this knowledge. Player a in turn is aware of this, and takes it into account when choosing.

% import uniform distributions :- use_module(library(lists)). %% basic distributions: players a and b both choose a number between 0 and 9 a(X) :- select_uniform(a,[0,1,2,3,4,5,6,7,8,9],X,_). b(X) :- select_uniform(b,[0,1,2,3,4,5,6,7,8,9],X,_). %% running the outer program assigns values to A and B state(A,B) :- a(A), subquery(b(B),P,[inner(A)]), % compute the distribution of the inner rejection query... pr(A,B,P). % ... and draw the value from it P::pr(A,B,P). % inner evidence, "observe"-style: run program with observation at end % player b sees player a's number, but believes they win if the sum of their numbers is greater than 8 inner(A) :- b(C), A+C > 8. % outer evidence, "observe"-style: run program with observation at end % the players win if their numbers sum to 13 win :- state(A,B), A+B =:= 13. % which number should a choose to win? query(a(_)). evidence(win).

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