1 - Introduction

Abstract

This chapter discusses many-sorted calculi and many-sorted language. The development of a many-sorted version of some given first-order one-sorted or unsorted calculus is well known in the area of formal logic. The first-order language has to be extended to a many-sorted language, the semantics for this language have to be defined, and the rules of inference have to be modified accordingly. Variable and function symbols are associated with a sort symbol, called the rangesort. The sort of a term is determined by the rangesort of its outermost symbol. This is a syntactic formulation of the fact that the object represented by a given term is a member of the subuniverse represented by the sort of that term. The syntactic requirement expresses the fact that not each term is meaningful as an argument to each function or predicate symbol. The definitions of the range and domain-sorts for the entire variable function and predicate symbols under consideration are collected in a so-called signature.