Introduction to Proof-theoretic Semantics
ESSLLI 2025 · Taught with Tao Gu
A five-day introductory course on proof-theoretic semantics (P-tS): an inferentialist alternative to the model-theoretic tradition, on which the meaning of a logical expression is constituted by the rules governing its use in proof rather than by reference to truth conditions in a model. The course was designed for graduate students, young researchers, and other non-specialists with a working knowledge of logic, and does not presuppose prior exposure to P-tS.
Across five lectures, the course develops the subject from first principles: proof theory and the shift from denotational to inferential semantics; Prawitz's theory of proof-theoretic validity; Sandqvist's base-extension semantics for classical and intuitionistic logic, and its connections to resolution calculi and logic programming; base-extension semantics for classical logic set against Kripke's model-theoretic semantics, and its extension to modal logic; and its extension to substructural logics, illustrated through intuitionistic multiplicative linear logic and inferentialist resource semantics.
Lecture Slides
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Lecture 1: General Proof TheoryWhat logic is, natural deduction and proof theory, and the shift from denotationalism to inferentialism as a theory of meaning.
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Lecture 2: Proof-theoretic ValidityPrawitz's normalization theorem and the analysis of proof-theoretic validity, including Prawitz's Conjecture.
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Lecture 3: Base-extension SemanticsSandqvist's base-extension semantics for classical and intuitionistic propositional logic, and its connections to resolution calculi and logic programming.
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Lecture 4: Classical Logic & Kripke SemanticsBase-extension semantics for classical logic set against Kripke's model-theoretic semantics, and its extension to modal and intuitionistic logic.
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Lecture 5: Substructural LogicBase-extension semantics for substructural logics, with intuitionistic multiplicative linear logic as a case study, and its application to inferentialist resource semantics.