Towards Polynomial Approximations of Full Propositional Logic

Abstract

The aim of this paper is to study a family of logics that approximates classical inference, in which every step in the approximation can be decided in polynomial time. For clausal logic, this task has been shown to be possible by Dalal [4,5]. However, Dalal’s approach cannot be applied to full classical logic. In this paper we provide a family of logics, called Limited Bivaluation Logics, via a semantic approach to approximation that applies to full classical logic. Two approximation families are built on it. One is parametric and can be used in a depth-first approximation of classical logic. The other follows Dalal’s spirit, and with a different technique we show that it performs at least as well as Dalal’s polynomial approach over clausal logic.