Bogdan Dicher (Centro de Filosofia, Universidade de Lisboa) 

Abstract:  Proof-theoretic semantics is a form of logical inferentialism, holding that the meaning of the logical constants is determined by the rules of inference which govern their behaviour in proofs. In this tradition, it is usually assumed that given a logical calculus, there always *exists* a *unique* relation that qualifies as a consequence relation. We argue that both of these two assumptions are incorrect. Nevertheless, this does not spell the end of the proof-theoretic project and the project is feasible provided one understands its aim as that of determining the meaning of the logical constants relative to a certain reflexive, monotonic, and transitive relation that can be uniquely determined using the Blok-Jonsson theory of abstract consequence relations. 
(Joint work with Francesco Paoli — University of Cagliari) 

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