The placeholder view of assumptions and the Curry–Howard correspondence

0546332 - FLÚ 2022 RIV NL eng J - Journal Article
Pezlar, Ivo
The placeholder view of assumptions and the Curry–Howard correspondence.
Synthese. Roč. 198, č. 11 (2021), s. 10109-10125. ISSN 0039-7857. E-ISSN 1573-0964
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
Impact factor: 1.595, year: 2021
Method of publishing: Limited access
https://doi.org/10.1007/s11229-020-02706-z

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as holes in proofs, either to be filled with closed proofs of the corresponding propositions via substitution or withdrawn as a side effect of some rule, thus in effect making them an auxiliary notion subservient to proper propositions.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. 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/11104/0322869