On Harmony and Metasequents

null, Bogdan Dicher (University of Lisbon)

The ALEF research group (Cluj-Napoca, Romania) announces an online talk by Bogdan Dicher (University of Lisbon) entitled "On Harmony and Metasequents". The talk is part of the group's regular seminar and takes place on Friday, DECEMBER 3, 18.00 EST (Eastern European Time). Please write to [email protected] or check our Facebook page (https://www.facebook.com/ALEF-100692348488914) if you want to participate. For more information about ALEF, as well as the schedule for the seminar in the 2021-2022 winter semester, please visit https://sites.google.com/view/alefgroupcluj.

Here is the abstract of the talk:

Proof-theoretic semantics is a branch of logical inferentialist according to which the meaning of the logical constants is determined by the primitive introduction and elimination rules which govern their behaviour in proofs. In previous work, this tenet is precisified and it is argued that this meaning determination is relative to the derivability relation between sequents in Gentzen systems, which is always reflexive, monotonic and transitive.

A salient ingredient of proof-theoretic semantics is the concept of harmony. This denotes a certain match between the inferential strength of the defining rules for a logical constant and it is arguably a sine qua non condition for a constant to be successfully defined by a set of rules. Despite its central role, the exact nature of harmony is a widely contested topic, even on standard conceptions of logical consequence.

In this talk we explore some of the challenges for developing a theory of harmony adequate for this reinterpretation of proof-theoretic semantics. The formal background is provided by a family of (sub)structural sequent calculi whose sequent-to-sequent derivability relation corresponds in a precise sense to the familiar consequence relations of Dunn-Belnap logic, strong Kleene logic, the logic of paradox, and of classical logic. Against this background, we investigate the behaviour of familiar pathological connectives such as Prior’s tonk and its dual knot and discuss their "disharmony", as well as the conception of harmony most apt to expose their defectiveness.