Probabilistic satisfiability and coherence checking through integer programming

•Paper offers solution to probabilistic satisfiability (PSAT) problems.•Proposed solution by reduction to integer linear programming.•Paper presents several variants of PSAT.•Paper deals with coherence checking by integer programming.•Paper shows empirical evidence of phase transition in PSAT.

This paper presents algorithms, both for probabilistic satisfiability and for coherence checking, that rely on reduction to integer programming. That is, we verify whether probabilistic assessments can be satisfied by standard probability measures (Kolmogorovian setting) or by full conditional probabilities (de Finettian coherence setting), and in both cases verify satisfiability or coherence using integer programming techniques. We present an empirical evaluation of our method, the results of which show evidence of phase transitions.