Puzzles of Existential Generalisation from Type-theoretic Perspective

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RACLAVSKÝ Jiří

Rok publikování 2022
Druh Článek ve sborníku
Konference Electronic Proceedings In Theoretical Computer Science (358)
Fakulta / Pracoviště MU

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Citace
www https://arxiv.org/pdf/2204.06726v1.pdf
Doi http://dx.doi.org/10.4204/EPTCS.358.6
Klíčová slova existential generalisation; quantifying in; explicit substitution; partial type logic; natural deduction
Popis 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.
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