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The Placeholder View of Assumptions and the Curry–Howard Correspondence (Extended Abstract)

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    SYSNO ASEP0546967
    Document TypeC - Proceedings Paper (int. conf.)
    R&D Document TypeThe record was not marked in the RIV
    TitleThe Placeholder View of Assumptions and the Curry–Howard Correspondence (Extended Abstract)
    Author(s) Pezlar, Ivo (FLU-F) ORCID, RID, SAI
    Source TitleLogic and Argumentation: 4th International Conference, CLAR 2021, Hangzhou, China, October 20–22, 2021, Proceedings. - Cham : Springer, 2021 / Baroni Pietro ; Benzmüller Christoph ; Wáng Yὶ N. - ISBN 978-3-030-89390-3
    Pagess. 513-520
    Number of pages8 s.
    Publication formPrint - P
    ActionCLAR 2021: International Conference on Logic and Argumentation /4./
    Event date20.10.2021 - 22.10.2021
    VEvent locationonline
    CountryCN - China
    Event typeWRD
    Languageeng - English
    CountryDE - Germany
    KeywordsPlaceholder view of assumptions ; Assumption withdrawing ; Curry–Howard correspondence ; Natural deduction ; Intuitionistic propositional logic
    Subject RIVAA - Philosophy ; Religion
    OECD categoryPhilosophy, History and Philosophy of science and technology
    R&D ProjectsGA19-12420S GA ČR - Czech Science Foundation (CSF)
    Institutional supportFLU-F - RVO:67985955
    UT WOS000754548600031
    EID SCOPUS85118158992
    DOI10.1007/978-3-030-89391-0_31
    AnnotationProofs from assumptions are amongst the most fundamental reasoning techniques. Yet the precise nature of assumptions is still an open topic. One of the most prominent conceptions is the placeholder view of assumptions generally associated with natural deduction for intuitionistic propositional logic. It views assumptions essentially as holes in proofs (either to be filled with closed proofs of the corresponding propositions via substitution or withdrawn as a side effect of some rule), thus in effect making them an auxiliary notion subservient to proper propositions. The Curry-Howard correspondence is typically viewed as a formal counterpart of this conception. In this talk, based on my paper of the same name (Synthese, 198(11), 10109–10125, 2021), I will argue against this position and show that even though the Curry-Howard correspondence typically accommodates the placeholder view of assumptions, it is rather a matter of choice, not a necessity, and that another more assumption-friendly view can be adopted.
    WorkplaceInstitute of Philosophy
    ContactChlumská Simona, chlumska@flu.cas.cz ; Tichá Zuzana, asep@flu.cas.cz Tel: 221 183 360
    Year of Publishing2022
Number of the records: 1  

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