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arXiv · 2301.02302

Proof-theoretic Semantics and Tactical Proof

Alexander V. Gheorghiu·David J. Pym
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Abstract

The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an \emph{argument}, broadly conceived as a certificate for a solution to the problem. Crucially, for such a certificate to be a solution, it has be \emph{valid}, and what makes it valid is that they are well-constructed according to a notion of inference for the underlying logical system. We provide a general framework uniformly describing the use of logic as a mathematics of reasoning in the above sense. We use proof-theoretic validity in the Dummett-Prawitz tradition to define validity of arguments, and use the theory of tactical proof to relate arguments, inference, and search.

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Alexander V. Gheorghiu, David J. Pym. 2023-01-05. Proof-theoretic Semantics and Tactical Proof. https://arxiv.org/abs/2301.02302

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