Incremental Theory Reasoning Methods forSemantic

Theory reasoning is an important technique for increasing the eeciency of automated deduction systems. In this paper we present incremental theory reasoning, a method that improves the interaction between the foreground reasoner and the background (theory) reasoner and, thus, the eeciency of the combined system. The use of incremental theory reasoning in free variable semantic tableaux and the cost reduction that can be achieved are discussed; as an example, completion-based equality reasoning is presented, including experimental data obtained using an implementation.