(Dis)connecting logical consequence and logical connectives

The Explanatory Inference Seminar is happy to announce its first session of the academic year, which will take place on the 29th of October, in Salle Ladrière, from 2 to 4 pm.

The speaker will be Pilar Terrés Villalonga from UCLouvain and her talk is entitled: (Dis)connecting logical consequence and logical connectives (see the abstract below).

Abstract :

The aim of this talk is to explore the connection between logical consequence and logical connectives in a calculus. It is well known that a presentation of a logic determines a behaviour for conjunctive and disjunctive combination, as well as for logical consequence. This can implicitly define a behaviour for conjunction, disjunction and conditional (following Dosen’s view of logical connectives as punctuation marks).

However, it is also possible to detach the behaviour of consequence from the behaviour of connectives. A natural way of doing so is via constitutional logics: I will present some traditional substructural logics using a novel presentation, constitutions for a logic, and I will motivate this constitutional presentation in comparison with natural deduction and Gentzen-style sequent calculus. I will show how logics presented via their constitutions can in a very natural way (i) present a substructural behaviour for logical consequence, while at the same time (ii) keep a classical behaviour for logical connectives. I will call those logics in which there are no connectives that behave as punctuation marks “unmatching logics”, while I will call “matching logics” those in which there are connectives that behave as punctuation marks.

Finally, I will indicate how to create constitutions that create matching logics for substructural logics such as relevant and linear logic, and I will explore the connections between matching and unmatching logics, given a particular behaviour for logical consequence.