# Masarykova univerzita

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# The Rule of Existential Generalisation, Its Derivability and Formal Semantics

Autoři 2021 Další prezentace na konferencích My contribution addresses various issues concerning the rule of existential generalisation (EG). My solutions are framed within a higher-order partial type theory $\mathsf{TT^*}$ that is equipped with a natural deduction system $\mathsf{ND_\mathsf{TT^*}}$. I derive (EG) from its primitive rules, especially the rule of existential quantifier introduction ($\exists$-I). Similarly for another derived rule ($\exists$-I$^\eta$). Substitution (t/x) of (EG) is fully and adequately specified inside the system and so (EG) is uniformly applicable within extensional, intensional and even hyperintensional contexts (we face no problems with quantifying in).

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