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The Placeholder View of Assumptions and the Curry–Howard Correspondence (Extended Abstract)
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SYSNO ASEP 0546967 Document Type C - Proceedings Paper (int. conf.) R&D Document Type The record was not marked in the RIV Title The Placeholder View of Assumptions and the Curry–Howard Correspondence (Extended Abstract) Author(s) Pezlar, Ivo (FLU-F) ORCID, RID, SAI Source Title Logic 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 Pages s. 513-520 Number of pages 8 s. Publication form Print - P Action CLAR 2021: International Conference on Logic and Argumentation /4./ Event date 20.10.2021 - 22.10.2021 VEvent location online Country CN - China Event type WRD Language eng - English Country DE - Germany Keywords Placeholder view of assumptions ; Assumption withdrawing ; Curry–Howard correspondence ; Natural deduction ; Intuitionistic propositional logic Subject RIV AA - Philosophy ; Religion OECD category Philosophy, History and Philosophy of science and technology R&D Projects GA19-12420S GA ČR - Czech Science Foundation (CSF) Institutional support FLU-F - RVO:67985955 UT WOS 000754548600031 EID SCOPUS 85118158992 DOI 10.1007/978-3-030-89391-0_31 Annotation Proofs 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as holes in proofs (either to be filled with closed proofs of the corresponding propositions via substitution or withdrawn as a side effect of some rule), thus in effect making them an auxiliary notion subservient to proper propositions.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. Workplace Institute of Philosophy Contact Chlumská Simona, chlumska@flu.cas.cz ; Tichá Zuzana, asep@flu.cas.cz Tel: 221 183 360 Year of Publishing 2022
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