Two Cases of Deduction with Non-referring Descriptions

TL;DR

This paper introduces a novel approach to formal reasoning with non-referring descriptions using partial type theory and natural deduction, addressing a gap in handling non-denoting terms in logical frameworks.

Contribution

It offers an alternative to existing methods by employing partial type theory, successfully formalizing deduction with non-referring descriptions and deriving presupposition rules.

Findings

Handles deduction with non-referring descriptions effectively.

Derives Strawsonian rules for existential presuppositions.

Provides a formal framework using partial type theory and natural deduction.

Abstract

Formal reasoning with non-denoting terms, esp. non-referring descriptions such as "the King of France", is still an under-investigated area. The recent exception being a series of papers e.g. by Indrzejczak, Zawidzki and K\"rbis. The present paper offers an alternative to their approach since instead of free logic and sequent calculus, it's framed in partial type theory with natural deduction in sequent style. Using a Montague- and Tich\'y-style formalization of natural language, the paper successfully handles deduction with intensional transitives whose complements are non-referring descriptions, and derives Strawsonian rules for existential presuppositions of sentences with such descriptions.