Semantic Tableaux for a Logic with Preorders and Dynamic Sorts

. In this paper we present a logic for dealing with preorders, where functions and predicates behave monotonically or antimonotonically in their arguments, and incorporating order-sorted relations into the syntax of the language. For this logic a ground tableaubased deduction method and a free variable extension version are proposed, proving their soundness and completeness. Finally, an implementation of the kernel of the logic based on logic programming is outlined. 1 Introduction The study of efficient methods for dealing with equality has been traditionally considered an important workline in different areas of theoretical computer science. However some recent research has revealed the need of extending this study in order to cover transitive relations different from those of equivalence. This is the case, for example, in CLP [JM 94], where constraint solving merges with logic programming. In the field of automated deduction this situation has resulted in the development of provers..