Metainferential Tableaux in the Many-valued Setting

AGUSTINA BORZI; AYLÉN BAVOSA CASTRO; BRUNO DA RÉ; JOAQUÍN TORANZO CALDERÓN; ARIEL ROFFÉ

Ciudad Autónoma de Buenos Aires

Workshop; Workshop on Logic and Philosophy of Logic; 2023

SADAF

Traditionally, a logic has always been identified with its set of valid inferences. However, recent developments in the field of substructural logics have challenged this idea (indirectly) by posing the question of whether classical logic (CL) and the mixed logic ST are the same logic, since they validate the same set of inferences. Nevertheless, there is a crucial difference between them: ST is a non-transitive system, since Cut fails in it, unlike CL. In a way, Cut says something about inferences, a property that CL has but ST does not. Presented as a rule, Cut is not an inference between formulae, but an inference between inferences, i.e., a metainference. This motivated several authors to work with this kind of apparatus, and more specifically, to develop metainferential logics. Most of this work is done from a model-theoretic perspective. In this talk, we shift to a proof-theoretic presentation, and formulate a general method for defining tableaux systems for metainferences of any level, for many well-known many-valued logics.