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Fusing Quantifiers and Connectives: is Intuitionistic Logic Different?
Stockholm University, Faculty of Humanities, Department of Philosophy.
2015 (English)In: Dag Prawitz on Proofs and Meaning / [ed] Heinrich Wansing, Cham: Springer, 2015, 259-280 p.Conference paper, Published paper (Refereed)
Abstract [en]

A paper by Dag Westerstahl and myself twenty years ago introduced operators that are both connectives and quantifiers. We introduced two binary operators that are classically interdefinable: one that fuses conjunction and existential quantification and one that fuses implication and universal quantification. We called the system PFO. A complete Gentzen-Prawitz style Natural Deduction axiomatization of classical PL was provided. For intuitionistic PL, however, it seemed that existential quantification should be fused with disjunction rather than with conjunction. Whether this was true, and if so why, were questions not answered at the time. Also, it seemed that there is no uniform definition of such a disjunctive-existential operator in classical PFO. This, too, remained a conjecture. In this paper, I return to these previously unresolved questions, and resolve them.

Place, publisher, year, edition, pages
Cham: Springer, 2015. 259-280 p.
Series
Outstanding Contributions to Logic, ISSN 2211-2758 ; 7
Keyword [en]
Anaphora, Axiomatization, Fusing operators, Intuitionistic logic, Natural deduction, Natural language, PFO, Prawitz, Predicate logic, Uniform definition, Unselective binding
National Category
Computer and Information Science Philosophy, Ethics and Religion
Identifiers
URN: urn:nbn:se:su:diva-119776DOI: 10.1007/978-3-319-11041-7_11ISI: 000357742900011ISBN: 978-3-319-11040-0 (print)ISBN: 978-3-319-11041-7 (print)OAI: oai:DiVA.org:su-119776DiVA: diva2:848168
Conference
Dag Prawitz on Proofs and Meaning Workshop, Bochum, Germany, September 10-11, 2012
Available from: 2015-08-24 Created: 2015-08-24 Last updated: 2016-11-22Bibliographically approved

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