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 E⁺, Maslov's class K, and Maslov's class DK of first-order logic. By the use of semantics-based translation methods we can embed the description logic ALB and extensions of the basic modal logic 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.