Puzzles of Existential Generalisation from Type-theoretic Perspective
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14210%2F22%3A00129199" target="_blank" >RIV/00216224:14210/22:00129199 - isvavai.cz</a>
Result on the web
<a href="https://arxiv.org/abs/2204.06726v1" target="_blank" >https://arxiv.org/abs/2204.06726v1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4204/EPTCS.358.6" target="_blank" >10.4204/EPTCS.358.6</a>
Alternative languages
Result language
angličtina
Original language name
Puzzles of Existential Generalisation from Type-theoretic Perspective
Original language description
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.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
60301 - Philosophy, History and Philosophy of science and technology
Result continuities
Project
<a href="/en/project/GA19-12420S" target="_blank" >GA19-12420S: Hyperintensional Meaning, Type Theory and Logical Deduction</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
10th International Conference on Non-Classical Logics. Theory and Applications (NCL 2022) Electronic Proceedings in Theoretical Computer Science (EPTCS) 358
ISBN
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ISSN
2075-2180
e-ISSN
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Number of pages
16
Pages from-to
68-83
Publisher name
Logic in Computer Science
Place of publication
Cornell Univeristy (USA), UNSW Austrálie
Event location
Lodz (PL)
Event date
Mar 14, 2022
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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