Two Cases of Deduction with Non-referring Descriptions
This work addresses a niche issue in formal logic and natural language semantics, offering an incremental improvement over existing methods.
The paper tackles the problem of formal reasoning with non-referring descriptions like 'the King of France' by proposing an alternative approach based on partial type theory and natural deduction in sequent style, successfully handling deduction with intensional transitives and deriving Strawsonian rules for existential presuppositions.
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 Krbis. 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 Tichý-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.