Contributions to the compositional semantics of first-order predicate logic

TL;DR

This paper extends Henkin, Monk, and Tarski's compositional semantics for first-order predicate logic by incorporating function symbols and defining the denotation of atomic formulas and terms compositionally.

Contribution

It introduces a compositional semantics for first-order logic that includes function symbols, enhancing the interpretative framework for atomic formulas and terms.

Findings

Denotation of atomic formulas as compositions of predicate symbols and arguments

Denotation of terms as compositions of function symbols and arguments

Extension of existing semantics to include function symbols

Abstract

Henkin, Monk and Tarski gave a compositional semantics for first-order predicate logic. We extend this work by including function symbols in the language and by giving the denotation of the atomic formula as a composition of the denotations of its predicate symbol and of its tuple of arguments. In addition we give the denotation of a term as a composition of the denotations of its function symbol and of its tuple of arguments.