Combining Resolution Decision Procedures

Abstract

We present resolution-based decision procedures for the guarded, two-variable and monadic fragments without equality in a uniform way and show how they can be combined. In this way, new decidable fragments are obtained. We make use of a novel technique for describing resolution decision procedures by means of clause schemes. The scheme notation provides a convenient way of specifying decision procedures, proving their correctness and analyzing complexity of associated decision problems. We also show that many decidability results obtained in the paper cannot be extended to the case with equality