Download PDFOpen PDF in browserTowards an Operational Proof-theoretic Semantics14 pages•Published: October 24, 2026AbstractModel-theoretic semantics comes with a computational counterpart: to check validity is to search for a countermodel, and tableaux, resolution, and satisfiability solvers make the semantics something one can run. Proof-theoretic semantics — the younger paradigm in which meaning is given by inferential role rather than by denotation — has no established counterpart. This paper proposes one: logic programming. We show that Sandqvist's base-extension semantics for intuitionistic propositional logic is executable in a precise sense. Bases are logic programs, and to each formula φ we assign a goal [[φ]] of a second-order hereditary Harrop language such that φ is supported in a base B exactly when [[φ]] is operationally derivable from B read as a program. The encoding is the Russell-Prawitz translation of the connectives with quantification restricted to atoms, and this restriction is not a limitation but the point: it is what the support clauses themselves demand. The correspondence is exact base by base, not merely at the level of validity, so that intuitionistic validity becomes the success of a single query against the empty program. Logic programming stands to proof-theoretic semantics as tableaux and satisfiability solvers stand to model-theoretic semantics.Keyphrases: base extension semantics, hereditary harrop formulae, inferentialism, intuitionistic logic, logic programming, proof theoretic semantics, tableaux, uniform proofs In: Stephan Schulz, Konstantin Korovin and Michael Rawson (editors). Proceedings of 16th International Workshop on the Implementation on Logics. Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning (short papers), vol 23, pages 30-43.
|
