Truth-value semantics and functional extensions for classical logic of partial terms based on equality

TL;DR

This paper develops a bottom-up truth-value semantics for classical logic with partial terms, demonstrating the conservativity of adding partial description and selection functions without strictness assumptions.

Contribution

It introduces a novel semantics framework for partial terms in classical logic, extending previous approaches with a bottom-up method.

Findings

Proves conservativity of partial description functions

Establishes semantics without strictness assumptions

Enhances understanding of partial term logic

Abstract

We develop a bottom-up approach to truth-value semantics for classical logic of partial terms based on equality and apply it to prove the conservativity of the addition of partial description and partial selection functions, independently of any strictness assumption.