Jiří Raclavský | Searcharxiv

arXiv2024

Two Cases of Deduction with Non-referring Descriptions

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.

cs.LO↗

arXiv2022

Puzzles of Existential Generalisation from Type-theoretic Perspective

The present paper addresses several puzzles related to the Rule of Existential Generalization, (EG). In solution to these puzzles from the viewpoint of simple type theory, I distinguish (EG) from a modified Rule of Existential Quantifier Introduction which is derivable from (EG). Both these rules are often confused and both are considered as primitive but I show that (EG) itself is derivable from the proper Rule of Existential Quantifier Introduction. Moreover, the latter rule must be primitive in logical systems that treat both total and partial functions, for the universal and the existential quantifiers are not interdefinable in them. An appropriate natural deduction for such a system is deployed. The present logical system is simpler than the system recently proposed and applied by the present author. It utilises an adequate definition of substitution which is capable of handling not only a higher-order quantification, but also (hyper)intensional contexts.

cs.LO↗