LLAL@GSIS (III)

Date & Venue

• Date: August 30, 2024.

• Venue: Room 310, Graduate School of Information Sciences, Tohoku University.  

Speakers

• Kaito Ichikura (Tohoku University)

• Satoshi Tojo (Asia University)

• Matteo Bizzarri (Scuola Normale Superiore)

Program

10:00--10:30 Kaito Ichikura "Continua of logics for negation below intuitionistic logic"

10:30--10:45 Break

10:45--11:45 Satoshi Tojo "Labelled Lambek Calculus for Tonal Music"

11:45--12:00 Break

12:00--13:00 Matteo Bizzarri "Framing Full Beliefs and Revisable Beliefs into Fractional Semantics for Classical Logic"

Abstracts

Kaito Ichikura: In this presentation, we analyse the effects of the principle of explosion (PE) and inference rules related to PE within the context of subminimal logics which were introduced by Dimiter Vakarelov.  In 1968, Yankov demonstrated the existence of a continuum of logics between classical logic and intuitionistic logic. Yankov's result suggests that there is a big gap between classical logic and intuitionistic logic, as indicated by the large cardinality of the logics existing between them. In 2020, Bezhanishvili, Colacito, and de Jong showed the existence of a continuum of logics among several subminimal logics using neighborhood semantics. This result implies that there are also big gaps among subsystems of intuitionistic logics which contain PE or axioms related to PE. Our main result is a generalization of the result by Bezhanishvili, Colacito, and de Jong, and we prove our result by a modified version of the algebraic method developed by Wroński in 1974. This presentation will briefly describe our findings.

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Satoshi Tojo: Categorial Grammar has been translated into Lambek Calculus, that is a variant of a sequent calculus. Into this formalism, we would embed a label, representing a possible world, for each formula. Thus far, we have been trapped by a traditional view of accessibility between different regions, that are keys, but on this occasion, we formally discuss what is the accessibility in regions, and extend the notion to include modes and atonal regions. Also, we discuss the frame property of modal operators and cut elimination.

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Matteo Bizzarri: The purpose of this talk is to present the results recently obtained in Fractional Semantics, a multi-valued semantics driven by purely proof-theoretic considerations with truth-values being the rational numbers in the closed interval [0,1]. Since its initial presentation, Fractional Semantics has produced different results. My aim is to expand Fractional Semantics by incorporating a set of beliefs, showing the application of this system and, furthermore, to find a way to distinguish between Full Beliefs and Revisable Beliefs. This idea is inspired by Hansson, who recently proposed a method for distinguishing between these types of beliefs using hyperreal numbers.