Resolution-Based Decision Procedures for Subclasses of First-Order Logic

Abstract

This thesis studies decidable fragments of first-order logic which are relevant to the field of non-classical logic and knowledge representation. We show that refinements of resolution based on suitable liftable orderings provide decision procedures for the subclasses \CE^+, $\overline{\mathrm{K}}$, and $\overline{\mathrm{DK}}$ of first-order logic. By the use of semantics-based translation methods we can embed the description logic $\mathcal{ALCR}$ and extensions of the basic modal logic $\mathsf{K}$ into fragments of first-order logic. We describe various decision procedures based on ordering refinements and selection functions for these fragments and show that a polynomial simulation of tableaux-based decision procedures for these logics is possible. In the final part of the thesis we develop a benchmark suite and perform an empirical analysis of various modal theorem provers