Satisfiability Machines

We propose a probabilistic model for formulas, in which a formula’s probability decreases with the number of pre-defined constraints it contradicts. Probability of ground conjunctions can be computed by a series of subsumption checks. The probability is equivalent (up to a multiplicative constant) to that computed by a Markov Logic Network for conjunctions that fully describe a possible world. An experiment indicates that the two quantities correlate also for other conjunctions, with less variance for larger conjunctions. The proposed framework suggests a simple classification principle.