Preface, p. vii Any reasonable logical system can be naturally translated into many-sorted first-order logic; thus many-sorted first-order logic is a universal logic. Since many-sorted logic can be translated into single-sorted first-order logic the latter is also universal. However, as will be seen in the course of this book, many-sorted logic faithfully interprets the semantics of the object ...

Order-sorted logic is a useful tool for knowledge representation and reasoning because it enables representation of sorted terms and formulas along with partially ordered sorts (called sort-hierarchy). However, this logic cannot represent more complex sorted expressions when they are true in any possible world (as rigid) or some possible worlds (as modality) such as time, space, belief, or situ...

The currying of term rewriting systems (TRSs) is a transformation of TRSs from a functional form to an applicative form. We have already introduced an order-sorted version of currying and proved that the compatibility and con uence of order-sorted TRSs were preserved by currying[3]. In this paper, we focus on a key property of TRSs, completeness. We rst show some proofs omitted in ref.[3]. Then...

Theories with hidden sorts provide a setting to study the idea of behaviour and behavioural equivalence of elements. But there are variants on the notion of theory: many sorted algebras, order sorted algebras and so on; we would like to use the theory of institutions to develop ideas of some generality. We formulate the notion of behavioural equivalence in a more abstract and categorical way, a...

An order-sorted logic can be regarded as a generalized first-order predicate logic that includes many and ordered sorts (i.e. a sort-hierarchy). In the fields of knowledge representation and AI, this logic with sort-hierarchy has been used to design a logic-based language appropriate for representing taxonomic knowledge. By incorporating the sort-hierarchy, order-sorted resolution and sorted lo...