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Proof-theoretic semantics, a problem with negation and prospects for modality. (English) Zbl 1426.03009

Summary: This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects for an account of the meanings of modal operators in terms of rules of inference.

MSC:

03A05 Philosophical and critical aspects of logic and foundations
03B45 Modal logic (including the logic of norms)
03F03 Proof theory in general (including proof-theoretic semantics)
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