DBPapers
DOI: 10.5593/sgem2017/21/S07.040

EXISTENTIAL GENERALIZATION IN TIL

M. Mensik, J. Kermaschek, L. Cienciala
Wednesday 13 September 2017 by Libadmin2017

References: 17th International Multidisciplinary Scientific GeoConference SGEM 2017, www.sgem.org, SGEM2017 Conference Proceedings, ISBN 978-619-7408-01-0 / ISSN 1314-2704, 29 June - 5 July, 2017, Vol. 17, Issue 21, 311-318 pp, DOI: 10.5593/sgem2017/21/S07.040

ABSTRACT

The paper deals with the fundamental rule of extensional logics, namely the rule of Existential Generalization. This rule can be applied in the situation when a function f is applied on its argument a to obtain the value of f at a. If the application does not fail, i.e., if the function f is defined at a, then we can existentially quantify, and derive that there is the value f(a). Our system is based on Transparent Intensional Logic (TIL). Since TIL is a hyperintensional, partial, typed lambda calculus, we examine the validity of the rule in TIL, or rather in its computational variant the TIL-Script language. The rule is context sensitive in the sense that depending on a context we should recognize the type of entity to be abstracted over. This is not to say that the rule can be invalid dependently on context; the rule is valid universally. Only that the type of the argument over which we quantity depends on the context. There are three kinds of contexts to be distinguished, namely extensional, intensional and hyperintensonal. We introduce the definition of these three kinds of context and an algorithm that recognizes in which context a particular construction occurs so that the Existential Generalization can be validly applied. The tool navigates users through the correct application of the deduction rules.

Keywords: Existential Generalization, TIL, logic, deduction, extension, intension, hyperintension

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