Advances in Proof-Theoretic Semantics [Hardcover]

This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory.

The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in T?bingen in 2013, where contributing authors were asked to provide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike.

Chapter 1. Introduction; Thomas Piecha & Peter-Schroeder-Heister.- Chapter 2. On Brouwer-Heyting-Kolmogorov provability semantics; Sergei N. Art?mov.- Chapter 3. Two Ways of General Proof Theory; Kosta Doaen.- Chapter 4. Generalised elimination rules; Roy Dyckhoff.- Chapter 5. On the proof theoretic foundations of set theory; Lars Halln?s.- Chapter 6. The choice of semantics as a methodological question; Wilfrid Hodges.- Chapter 7. The mode of presentation; Reinhard Kahle.- Chapter 8. Remarks on relations between Gentzen and Heyting inspired PTS; Dag Prawitz.- Chapter 9. Unification of logics by reflection; Giovanni Sambin.- Chapter 10. BHK and Brouwer's Theory of the Creative Subject; G?ran Sundholm.- Chapter l£P