Proof-theoretic Semantics and Tactical Proof

TL;DR

This paper introduces a unified framework for understanding problem-solving using logic, emphasizing proof-theoretic validity and tactical proof to connect arguments, inference, and search processes.

Contribution

It develops a general, uniform framework based on proof-theoretic validity and tactical proof to model reasoning and problem-solving in logical systems.

Findings

Defines a notion of validity for arguments based on proof-theoretic principles

Relates arguments, inference, and search through tactical proof theory

Provides a comprehensive framework for logic-based problem-solving

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.