This paper presents the first heuristic method for solving the satisfiability problem in the logic with approximate conditional probabilities. This logic is very suitable for representing and reasoning with uncertain knowledge and for modeling default reasoning. The solution space consists of variables, which are arrays of 0 and 1 and the associated probabilities. These probabilities belong to a recursive non-Archimedean Hardy field which contains all rational functions of a fixed positive infinitesimal. Our method is based on the bee colony optimizationmeta-heuristic. The proposed procedure chooses variables from the solution space and determines their probabilities combining some other fast heuristics for solving the obtained linear system of inequalities. Experimental evaluation shows a high percentage of success in proving the satisfiability of randomly generated formulas. We have also showed great advantage in using a heuristic approach compared to standard linear solver. 
Bee colony optimization for the satisfiability problem in probabilistic logic