II Workshop on Logic and Philosophy of Logic

Federico Pailos: “Naıve non-substructural solutions to the Validity Paradox”

We present naive non-substructural solutions to the Validity Paradox. The main idea behind these solutions is to break up the link between a valuation satisfying an inference and a valuation not being a counterexample to that inference. A philosophical consequence of this technical move is that, in some of these theories, VD will be valid while at the same time invalid, while in others VD won’t be invalid, though it will not be valid either. No matter what path is chosen, it will not be possible to have the problematic instances of VD as axioms of the derivations that lead to the paradoxical result. The first one cannot have them as axioms because the problematic instances are not valid, and the second one cannot have them either because they are invalid. Given the details of these proposals, new forms of both (i) naıve validity and (ii) non-substructurality arise.

Aylén Bavosa Castro: “Metainferential Tableaux in the Many-valued Setting”

For this presentation, we will introduce a scheme for defining labelled tableaux calculi for metainferences of any level n. We will also explain how to get the best possible scenario in terms of computational efficiency and will also present correctness and completeness results. The main advantage of our presentation is that it is completely broad since it provides general rules, independent of the schema or set of valuations of the inferential logics, but can be complemented with operational rules accordingly.

This is joint work with Agustina Borzi, Bruno Da Ré, Ariel Roffe, and Joaquin Toranzo.

Edson Bezerra: “A validity theory for the ST-hierarchy”

The hierarchy of metainferences STω has garnered significant attention in the literature due to its ability to recover as many classical metainferences as possible. In this talk, we introduce a fixed-point validity predicate for STω. Subsequently, we demonstrate not only that this predicate captures all valid metainferences according to STω logic but also the naïve principles governing validity. The resulting theory of validity is non-trivial, and it can internalize its valid metainferences.

This is joint work with Eduardo Barrio and Federico Pailos.

Dave Ripley: Probabilistic consequence relations

Classical probability distributions over a propositional language are certain ways of assigning numbers from the real interval from 0 to 1 to sentences. In this work, we treat these classical probability distributions as in effect being valuations in a many-valued logic, and we explore a range of consequence relations that can be defined over them.

This is joint work with Paul Égré.