Probable consistency checking for sets of propositional clauses

Abstract

Inconsistencies inevitably arise in knowledge during practical reasoning. In a logic-based approach, this gives rise to the need for consistency checking. Unfortunately, this can be difficult. In classical propositional logic, this is intractable. However, there is a useful alternative to the notion of consistency called probable consistency. This offers a weakening of classical consistency checking where polynomial time tests are done on a set of formulae to determine the probability that the set of formulae is consistent. In this paper, we present a framework for probable consistency checking for sets of clauses, and analyse some classes of polynomial time tests.