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

0546967 - FLÚ 2022 DE eng C - Conference Paper (international conference)
Pezlar, Ivo
The Placeholder View of Assumptions and the Curry–Howard Correspondence (Extended Abstract).
Logic and Argumentation: 4th International Conference, CLAR 2021, Hangzhou, China, October 20–22, 2021, Proceedings. Cham: Springer, 2021 - (Baroni, P.; Benzmüller, C.; Wáng, Y.), s. 513-520. Lecture Notes in Artificial Intelligence, 13040. ISBN 978-3-030-89390-3.
[CLAR 2021: International Conference on Logic and Argumentation /4./. online (CN), 20.10.2021-22.10.2021]
R&D Projects: GA ČR(CZ) GA19-12420S
Institutional support: RVO:67985955
Keywords : Placeholder view of assumptions * Assumption withdrawing * Curry–Howard correspondence * Natural deduction * Intuitionistic propositional logic
OECD category: Philosophy, History and Philosophy of science and technology
https://doi.org/10.1007/978-3-030-89391-0_31

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as holes in proofs (either to be filled with closed proofs of the corresponding propositions via substitution or withdrawn as a side effect of some rule), thus in effect making them an auxiliary notion subservient to proper propositions.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.
Permanent Link: http://hdl.handle.net/11104/0323339