Generalized probabilistic satisfiability through integer programming

Abstract

This paper studies the generalized probabilistic satisfiability (GPSAT) problem, where the probabilistic satisfiability (PSAT) problem is extended by allowing Boolean combinations of probabilistic assertions and nested probabilistic formulas. We introduce a normal form for this problem and show that both nesting of probabilities and multi-agent probabilities do not increase the expressivity of GPSAT. An algorithm to solve GPSAT instances in the normal form via mixed integer linear programming is proposed. The implementation of the algorithm is used to explore the complexity profile of GPSAT, and it shows evidence of phase-transition phenomena. Even though GPSAT is considerably more expressive than PSAT, it can be handled using integer linear programming techniques.