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

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.

November

1999