LLAL@GSIS (VII)

Date & Venue

• Date: July 5, 2025.

• Venue: Room 207, Graduate School of Information Sciences, Tohoku University.  

Speakers

• Sankha S. Basu (IIIT-Dehli)

• Takako Nemoto (Tohoku University)

• Satoru Niki (Kanagawa University)

• Tyko Schuff (MCMP)

• Masanobu Toyooka (Tohoku University) 

Program

10:45--11:45 Tyko Schuff "Meaning-Variance Reconsidered"

11:45--12:00 Break

12:00--13:00 Masanobu Toyooka "A Solution to Collapsing Problem and an Inferentialist Approach to Intuitionistic and Classical Connectives"

13:00--14:00 Lunch 

14:00--15:00 Satoru Niki "Canonizing Canonical Negation" 

15:00--15:15 Break

15:15--16:15 Takako Nemoto "0=1 in minimal set theory"

16:15--16:30 Break

16:30--17:30 Sankha S Basu "Relational companions of logics"

Abstracts

Sankha S Basu: The variable inclusion companions of logics have lately been thoroughly studied by multiple authors. There are broadly two types of these companions: the left and the right variable inclusion companions. Another type of companions of logics induced by Hilbert-style presentations (Hilbert-style logics) were introduced in a recent paper. A sufficient condition for the restricted rules companion of a Hilbert-style logic to coincide with its left variable inclusion companion was proved there, while a necessary condition remained elusive. This talk will be roughly divided into two parts. In the first part, I will present a necessary and sufficient condition for the left variable inclusion and the restricted rules companions of a Hilbert-style logic to coincide. The second part of the talk relies on the observation that the variable inclusion restrictions used to define variable inclusion companions of a logic $(L,\vdash)$ are relations from the power set of  $L$ to $L$. This leads to a more general idea of a relational companion of a logical structure, a framework that we borrow from the field of universal logic. Properties of relational companions of logics can be shown to depend on the relations used to define them. Finally, it can be shown that even Hilbert-style logics and the restricted rules companions of these can be brought under the umbrella of the general notions of logical structures and their relational companions. 

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Takako Nemoto: It is well known that, for any formula A in the language of arithmetic, 0=1\to A is provable in arithmetic over minimal logic. It shows that even without assuming the principle of explosion, we have something similar in arithmetic. In this talk, we consider that 0=1 in set theory over minimal logic has the same property. We will see which axiom of set theory is essential for it. This is a joint work with Peter Schuster.

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Satoru Niki: Abelian logic, introduced by E. Casari, R. K. Meyer and J. Slaney, is often categorised as belonging to a family of logics proving contradictions: negation inconsistent logics. The membership is indeed claimed by committing to some of the most extreme cases of contradiction, such as ''A implies A'' and its negation. This feature makes Abelian logic appear rather peculiar. On the other hand, there are some grounds to doubt if the standard negation of the logic, called ''canonical negation'', is really a negation. In this talk, we introduce a few alternative semantics, borrowing ideas from the American plan for negation, in order to give an apology for the status of canonical negation as a negation. (j.w.w. Heinrich Wansing)

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Tyko Schuff: Our intent is to reframe and explicate the Quinean notion of meaning variance in logic. We start from the idea that different logics preserve different properties from premises to conclusion in their valid arguments. This variance with respect to what is being preserved by a given logic then implies meaning variance with regard to the logical constants and the relation of logical consequence itself. But beyond simply just arguing that there must be some meaning variance between logics, our approach allows us to point out the root cause of the phenomenon and to document the change in meaning in much closer detail: Why is there a change of meaning from one logic to another, what exactly is changing and what does it change from and to. In this regard we hope our account offers an improvement over Quine’s original argument.

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Masanobu Toyooka: The collapsing problem, which was first pointed out by Popper (1948), is a well-known problem especially in the context of dealing with intuitionistic and classical logics.There are many ways to avoid falling into this problem, and the approach taken in this talk is based on the ways of Humberstone (1979), del Cerro & Herzig (1996), and Lucio (2000). To put it more concretely, we newly propose a sequent calculus for the logic studied in the three papers. Our sequent calculus uses the ordinary notion of a sequent and enjoys the cut elimination and the subformula property. Moreover, by providing a sequent calculus, we can tackle the following question: How should intuitionistic (classical) inferentialist view classical (intuitionistic) logical connectives? We would like to give a suggestion about this question, following the treatment of Restall (2005, 2009) with the modification that employs the method in Takano (2016), although it is probably not a perfect answer.

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Acknowledgement

This workshop is partially supported by Japan Society for the Promotion of Science (JSPS) through grant 24K21344.