Advances in Proof-Theoretic Semantics

Thomas Piecha graduated both in Philosophy and in Physics,and holds a Ph.D. in Computer Science. He has published on proof-theoretic and dialogical approaches in logic, and currently works on the proof-theoretic analysis of hypothetical reasoning. Peter Schroeder-Heister is professor of logic and philosophy of language at the University of Tübingen, holding a joint appointment in the Departments of Philosophy and of Computer Science. He works in particular on philosophical aspects of proof theory and is a leading expert in the area of proof-theoretic semantics.

Chapter 1. Introduction; Thomas Piecha & Peter-Schroeder-Heister.- Chapter 2. On Brouwer-Heyting-Kolmogorov provability semantics; Sergei N. Artëmov.- Chapter 3. Two Ways of General Proof Theory; Kosta Dosen.- Chapter 4. Generalised elimination rules; Roy Dyckhoff.- Chapter 5. On the proof theoretic foundations of set theory; Lars Hallnäs.- 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; Göran Sundholm.- Chapter 11. Compositional semantics for predicate logic: Eliminating bound variables from formulas and deductions; William W. Tait.- Chapter 12. Intuitionism, the Paradox of Knowability and Empirical Negation; Gabriele Usberti.- Chapter 13. Explicit composition and its application in normalization proofs; Jan von Plato.- Chapter 14. A two-sorted typed lambda-calculus; Heinrich Wansing.- Chapter 15. Kreisel's second clause and the Theory of Constructions; Walter Dean & Hidenori Kurokawa.- Chapter 16. On Paradoxes in Proof-Theoretic Semantics; Yoshihiro Maruyama.