LLAL@GSIS (IX)

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 Thomas Ågotnes' visit to Sendai, some special emphasis is laid on topics related to modalities.

Date & Venue

• Date: October 28, 2025.

• Venue: Lecture Room on 3F , Graduate School of Information Sciences, Tohoku University.  

Speakers

• Thomas Ågotnes (University of Bergen)

• Leonardo Pacheco (Institute of Science Tokyo) 

• Masanobu Toyooka (Tohoku University) 

Program

15:30--16:30 Masanobu Toyooka "Generalizing subintuitionistic logics over neighborhood semantics"

16:30--16:45 Break 

16:45--17:45 Leonardo Pacheco "Intuitionistic Knowledge as a Constructive Diamond" 

17:45--18:00 Break

18:00--19:15 Thomas Ågotnes "Weakening distribution over conjunction in modal logics, with two applications in epistemic logic"

Abstracts

Thomas Ågotnes: In normal modal logics the box modality distributes over conjunction. Weakening the equivalence in one direction we get non-monotonic modal logics. In the talk we look at a particular weakening of monotonicity by a rule we call the interpolation rule. We demonstrate an application in epistemic logic: the interpolation rule characterises the logic of "secretly-knowing". Weakening the equivalence in the other direction we get non-adjunctive modal logics. We look at a particular weakening of conjunctive closure - "weak" conjunctive closure. Again, we show an application in epistemic logic: weak conjunctive closure characterises the notion of "somebody-knows". In both cases we present completeness and other meta-logical results.

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Leonardo Pacheco: Artemov and Protopopescu introduced IEL, a modal extension of intuitionistic propositional logic with a modal operator K, standing for knowledge. The K operator is governed by two characteristic axioms: P -> KP and KP -> ~~P. We define and study an alternative semantics for IEL where K is evaluated as a constructive diamond. We show completeness and FMP for our semantics. For applications, we have the following: we separate intuitionistic knowledge and intuitionistic belief; we discuss the relation between Glivenko's Theorem and ignorance; we show that in some sense IEL is indeed intuitionistic, but in another sense it is not. (This is joint work with Igor Sedlár, Czech Academy of Science)

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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 the Graduate School of Information Sciences, Tohoku University.