Zoom Link - PTS-Seminar: Masanobu Toyooka (Tohoku University), Dec 9, 11am (UTC+0)

[PTS Network]

Dear all,

The sixth session of the Proof-Theoretic Semantics Seminar Series is coming up!

This is a series of periodic online talks delivered by early career researchers working in proof-theoretic semantics or akin fields, organised by the PTS-Network.

Here's the zoom link for tomorrow:

Link: https://zoom.us/j/95090289330

ID: 95090289330

On Tuesday, December 9, 11am (UTC+0) Masanobu Toyooka (Tohoku University) will present his work with the title "Categoricity and Expressibility of Classical Connectives".

Here is the abstract:
"This talk explores the categoricity and the expressibility of classical connectives, inspired by the studies of Carnap, Gabbay, and Garson. In 1943, Carnap observed that the classical single-succedent consequence relation did not ``carve out'' the two-valued truth table of disjunction, implication, or negation. This phenomenon, which is currently called ``the categoricity problem'', may be regarded as problematic for a moderate inferentialist who advocates classical logic but refuses semantic holism. Gabbay (1978) generalized Carnap's study and dealt with an arbitrary n-place connective having the two-valued truth table. In the paper, the existence of a single-succedent consequence relation that carves out the truth table of a connective is investigated.

After the studies of Carnap and Gabbay, Garson (2001, 2010) investigated which semantic clause was carved out by the set of rules for a connective in the natural deduction system rather than by the classical single-succedent consequence relation. In order to interpret a rule, two different measures were considered: ``global measure'' and ``local measure''. Garson revealed that these two measures carved out different semantic clauses for a connective.

This talk deals with an arbitrary n-place connective having the two-valued truth table and observes the possibility of carving out the truth table, as Gabbay did. However, our approach diverges from Gabbay's one in the following two points: (i) we work not only on a consequence relation but also on a rule, as Garson did, both global and local measures being employed to interpret it; (ii) we do not limit our attention to single-succedent syntactic objects but introduce four different forms of syntactic objects. These treatments generate various benchmarks of the possibility of carving out the two-valued truth table for a connective. In the conclusion, it is revealed which connective has the two-valued truth table that can be carved out according to each benchmark."


All the best,
Sara Ayhan, Hermógenes Oliveira, Antonio Piccolomini d'Aragona & Will Stafford