Language and Logic advanced course:
Proof-Theoretic Semantics.


Course material: proof_theoretic_semantics.html


Proof-Theoretic Semantics (PTS) is an alternative to model-theoretic (or truth-condition) semantics. It is based on the idea that the central notion in terms of which meanings are assigned to expressions is that of proof rather than truth. In this sense PTS is inferential rather than denotational in spirit. Although the claim that meaning is use has been quite prominent in philosophy for more than half a century, the model-theoretic approach has always dominated formal semantics. However, within general proof theory several formal approaches to PTS have been developed which promise to provide an alternative to the model-theoretic approach. After recalling certain basics from proof theory of natural deduction, this tutorial presents traditional approaches to PTS in the spirit of Dummett, Prawitz and Martin-Löf as well as advanced conceptions based on "definitional reasoning" based on work of the author.