LLAL@GSIS (VIII)

Aim

The aim of this edition of LLAL@GSIS meeting is to discuss and exchange new ideas and recent developments related to philosophical logic and philosophy of logic, broadly construed. Given that the meeting is planned on the occasion of Jan Sprenger's visit to Sendai, some special emphasis is laid on topics related to the conditionals.

Date & Venue

• Date: August 25, 2025.

• Venue: Room 711, Graduate School of Information Sciences, Tohoku University.  

Speakers

• Satoru Niki (Kanagawa University)

• Hitoshi Omori (Tohoku University)

• Jan Sprenger (University of Turin)

• Masanobu Toyooka (Tohoku University) 

Program

10:00--12:00 Discussion

12:00--13:30 Lunch

13:30--14:30 Hitoshi Omori "A note on Sasaki's conditional in view of Garson's question"

14:30--14:45 Break

14:45--15:45 Masanobu Toyooka "Generalizing subintuitionistic logics over neighborhood semantics" [cancelled due to illness]

15:45--16:00 Break 

16:00--17:00 Satoru Niki "Analyses of contradictions in relevant connexive logics" 

17:00--17:15 Break

17:15--18:30 Jan Sprenger "Trivalent Conditionals and Negation"

Abstracts

Satoru Niki: Nissim Francez and Yale Weiss introduced relevant connexive logics following the strategy of Heinrich Wansing's constructive connexive logic. An implication of which is that the systems are negation inconsistent: they contain as theorems pairs of a formula and its negation. In this talk, in order to shed lights on this unusual phenomenon, I will discuss two necessary conditions such provable contradictions must satisfy.

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Hitoshi Omori: In 1994, Akinori Sasaki introduced an expansion of classical logic obtained by adding a binary connective which is designed to generalize the treatment of conditionals in both conditional logic as well as relevance logic. This is interesting since it can be seen as echoing a theme briefly mentioned in passing by James Garson much later in `Modal logic for philosophers'. Given that Sasaki's results are published only in Japanese, the first aim of this discussion note is to report Sasaki's results for a wider audience beyond the Japanese community. Moreover, since a closer inspection reveals that Sasaki's proposal is not without problems, I will present a few modifications of Sasaki's proposal that might be worth exploring towards a satisfactory answer to Garson's question.

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Jan Sprenger: This paper studies conditional negation starting from the idea that indicative conditionals express conditional assertions and have trivalent valuations. Paired with the idea that valid inference preserves acceptance of the premises, this view yields a negation-inconsistent, contra-classical logic of conditionals. It allows to reconstruct the idea that there are essentially two forms of negating an assertion in natural language: denying the semantic content of an assertion A (i.e., commit to ¬A), and refusing to add A to the common ground of the conversation.

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Masanobu Toyooka: This talk generalizes subintuitionistic logics over the neighborhood semantics. A subintuitionistic logic is a logic semantically obtained by dropping one, some, or none of reflexivity, transitivity, and persistency over the Kripke semantics for intuitionistic propositional logic. Subintuitionistic logics were originally studied in (Visser 1981), (Corsi 1987), and (Dosen 1993), after which in (Restall 1994) they were studied over different consequence relation inspired by the semantics for relevant logics. As it is known that the modal logic K, the weakest logic over the Kripke semantics for modal logics, can be generalized over the neighborhood semantics, it is a natural direction of investigation to generalize subintuitionistic logics over the neighborhood semantics. This investigation was carried out by (Shirmohammadzadeh Maleki & de Jongh 2017). However, the consequence relation introduced in (Restall 1994) was not treated in the paper. This talk generalizes subintuitionistic logics over the neighborhood semantics with respect to the consequence relation in (Restall 1994). We not only semantically reveal the relationship between this consequence relation and the one studied in (Shirmohammadzadeh Maleki & de Jongh 2017) but also provide the Hilbert system that is sound and strongly complete to the consequence relation in (Restall 1994). In addition, we deal with the two extensions by the axioms (D) and (T), provided in (Corsi 1987).

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Acknowledgement

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