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Single-Assumption Systems in Proof-Theoretic Semantics

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Abstract

Proof-theoretic semantics is an inferentialist theory of meaning, usually developed in a multiple-assumption and single-conclusion framework. In that framework, this theory seems unable to justify classical logic, so some authors have proposed a multiple-conclusion reformulation to accomplish this goal. In the first part of this paper, the debate originated by this proposal is briefly exposed and used to defend the diverging opinion that proof-theoretic semantics should always endorse a single-assumption and single-conclusion framework. In order to adopt this approach some of its criteria of validity, especially separability, need to be weakened. This choice is evaluated and defended. The main argument in this direction is based on the circular dependences of meaning between multiple assumptions and conjunctions, and between multiple conclusions and disjunctions. In the second part of this paper, some systems that suit the new requirements are proposed for both intuitionistic and classical logic. A proof that they are valid, according to the weakened criteria, is sketched.

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Acknowledgements

I want to thank Prof. Enrico Moriconi for helpful discussions on the issues of this paper, Prof. Nissim Francez for very honest and informative feedback on an early version of it, and Prof. Alberto Naibo for suggesting me some interesting developments. I also would like to thank Prof. Peter Milne for some useful comments on an early manuscript that formed the main part of this paper, and the anonymous reviewers who helped me greatly in the revision process. Of course, only I am to blame for any remaining errors.

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  1. Department of Civilisations and Forms of Knowledge, Università di Pisa, Pisa, Italy

    Leonardo Ceragioli

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  1. Leonardo Ceragioli
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Correspondence to Leonardo Ceragioli.

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Ceragioli, L. Single-Assumption Systems in Proof-Theoretic Semantics. J Philos Logic 51, 1019–1054 (2022). https://doi.org/10.1007/s10992-022-09658-4

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