Composition of Deductions within the Propositions-As-Types Paradigm

Abstract

Kosta Dosen argued in his papers Inferential Semantics Dosen (in Inferential semantics, Springer, Berlin 2015) and On the Paths of Categories Dosen (in On the paths of categories, Springer, Cham 2016) that the propositions-as-types paradigm is less suited for general proof theory because—unlike proof theory based on category theory—it emphasizes categorical proofs over hypothetical inferences. One specific instance of this, Dosen points out, is that the Curry–Howard isomorphism makes the associativity of deduction composition invisible. We will show that this is not necessarily the case.