This workshop is part of the project titled Collaborative Research on Logic of Agent: From Non-classical Perspectives supported by the SP+ Fund of Kyoto University designed to strengthen the collaboration between Kyoto University and National Taiwan University. The title "Logic of Agent" reflects a shift in the field of logic from traditional formal reasoning studies towards a focus on more agentative aspects of human intellectual activities, such as knowledge, belief, action, and decision-making. This workshop is the second meeting following the first session held in Taipei in October 2024. It is co-hosted with the KAKENHI project 24K03359.
Date March 1 and 2, 2025
Venue Seminar roon on the 1st floor of Maskawa Building for Education and Research (No.13 of Campus map)
Speakers
Sara Ayhan (Ruhr University Bochum)
Matteo Bizzarri (Scuola Normale Superiore)
Peter Hawke (Lingnan University)
Yuichiro Hosokawa (Gunma Prefectural Women's University)
Hitoshi Omori (Tohoku University)
Takuro Onishi (Kyoto University)
Katsuhiko Sano (Hokkaido University)
Shuhei Shimamura (Hiroshima University)
Shawn Standefer (National Taiwan University)
Masanobu Toyooka (Hokkaido University)
Ren-June Wang (National Chung Cheng University)
Program
March 1
9:15--9:20 Opening
9:20--10:20 Shawn Standefer
10:20--11:20 Yuichiro Hosokawa
11:20--12:20 Ren-June Wang
12:20--13:30 Lunch
13:30--14:30 Shuhei Shimamura
14:30--14:45 Break
14:45--15:45 Peter Hawke
15:45--16:45 Takuro Onishi
March 2
9:30--10:30 Matteo Bizzarri
10:30--11:30 Masanobu Toyooka
11:30--12:30 Katsuhiko Sano
12:30--14:00 Lunch
14:00--15:00 Sara Ayhan
15:00--16:00 Hitoshi Omori
16:00--16:05 Closing
Titles and abstracts
Shawn Standefer (National Taiwan University)
Title: On hyperintenisonality in relevant logics
Abstract: In this talk, we present a definition of a hyperintensionality appropriate to relevant logics. We then show that relevant logics are hyperintensional in this sense, drawing consequences for other non-classical logics, including some substructural logics. We further prove results concerning extensionality in relevant logics. We close by discussing related concepts for classifying formula contexts and potential applications of these results.
Yuichiro Hosokawa (Gunma Prefectural Women's University)
Title: A New Reconstruction of Reichenbach’s Tense Theory in a New Hybrid Extension of Prior’s Tense Logic
Abstract: Prior’s Past, Present, and Future (1967) makes a series of destructive comments on Reichenbach’s tense theory (1947). To put the points of the Prior’s criticism of Reichenbach in order, (1) Reichenbach’s tense theory is too simple, (2) Reichenbach's tense theory is too complex, and (3) Reichenbach’s tense theory cannot distinguish the simple past and the present perfect. The conclusion of this presentation is as follows. Firstly, we, together with Blackburn & Jørgensen (2016), completely agree on (1). Secondly, Blackburn & Jørgensen (2016) disproved (2). Finally, we disprove (3) and demonstrate the contrary: Reichenbach's distinction between the simple past and the present perfect can be reconstructed in a new hybrid extension HTLTC of Prior's Tense Logic in a refined and sophisticated manner.
Ren-June Wang (National Chung Cheng University)
Title: A Normal Form for Intuitionistic Sequent Calculus
Abstract: The cut elimination theorem is a type of normal form theorem, stating that every sequent proof without assumptions can be transformed into a cut-free proof. In this talk, we explore a more general concept of normal form for intuitionistic sequent calculus, which also applies to proofs with assumptions. We present a normalization procedure based on this concept. Since cut-free proofs are a special case of normal proofs in our framework, our normalization procedure, when applied to assumption-free proofs, provides an alternative cut elimination procedure.
Shuhei Shimamura (Hiroshima University)
Title: Relevance as Minimality: A Logical Expressivist Approach
Abstract: Relevance in various types of nonlogical inferences has sometimes come to fore under the names, such as evidential relevance, explanatory/causal relevance, legal relevance, practical/moral relevance, and pragmatic relevance. This talk submits a notion that aims to capture what is at the core of these uses of the term “relevance” concerning various nonlogical inferences. The intuitive idea, which I shall defend and develop, is roughly put as follows: an inference is relevant if it contains no redundant premise. I call this general notion of relevance minimality. I offer a formal system in which the notion of minimality is defined and expressed by a special logical operator, [M]X. This system also makes it possible to compare minimality to a more orthodox notion of relevance, deductive usability, which has been closely studied by relevance logicians. It turns out that while minimality, like deductive usability, satisfies criteria of relevance widely accepted by relevance logicians, it is stronger than that familiar notion in several interesting manners.
Peter Hawke (Lingnan University)
Title: Stable Acceptance Semantics and Modal Knowledge
Abstract: We start by observing some puzzling linguistic data concerning ordinary knowledge ascriptions that embed an epistemic (im)possibility claim. We conclude that it is untenable to jointly endorse both the (classical) principle that entailment is preserved under contraposition and a pair of intuitively attractive theses about knowledge ascriptions: the thesis that knowledge ascriptions are always veridical and a ‘negative transparency’ thesis that reduces knowledge of a simple negated ‘might’ claim to an epistemic claim without modal content. We motivate a strategy for answering the trade-off: preserve veridicality and (generalized) negative transparency, while abandoning the general validity of contraposition. We survey and criticize various approaches for incorporating veridicality into domain semantics, a paradigmatic ‘information-sensitive’ framework for capturing negative transparency and, more generally, the non-classical behavior of sentences with epistemic modals. We then present a novel information-sensitive semantics that successfully executes our favored strategy: stable acceptance semantics. Finally, we observe paraconsistent features of the system that motivate further investigation.
Takuro Onishi (Kyoto University)
Title: Double de Morgan negation as positive modality
Abstract: Double negation forms positive modality. For example, Dosen (1984) considers double intuitionistic negation as a necessity operator. Double de Morgan (relevant) negation of course forms a modality, but due to double negation laws it is just a trivial modality. In this talk I will consider the positive modality defined as a composition of two different de Morgan negations, and by constructing such a modality from negative modalities (impossibility and unnecessity), specify its logic.
Matteo Bizzarri (Scuola Normale Superiore)
Title: Extending Fractional Semantics: Full and Revisable Beliefs
Abstract: 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. Additionally, I will discuss how Fractional Semantics relates to Belief Revision and explore possible ways of integrating revision mechanisms into the framework. While my results in this area are still preliminary, I will outline some directions for future work and potential connections with existing models of belief change.
Toyooka Masanobu (Hokkaido University)
Title: Humberstone's logic as an extension of minimal logic
Abstract: The aim of this presentation is to provide the semantics of Humberstone's logic, which is different from the original one. Humberstone (2006) added a special constant, denoted by ``Ω'', to positive intuitionistic propositional logic. The resulting logic has the Kripke semantics, where the following two conditions are imposed on a model: (i) an accessibility relation equipped with a model must be a partial order, not a quasi-order; (ii) a model must be rooted. In this semantics, given a Kripke model, Ω is true in a state iff the state is different from the root of the model. Since, in the Kripke semantics for intuitionistic logic, an accessibility relation equipped with a model can be a quasi-order and a model need not be rooted, it is a natural question to ask whether we can alleviate (i) and drop (ii). This presentation answers this question affirmatively. We first prove that (i) can be alleviated and then proceed to explain that (ii) can be dropped by employing the Q-semantics for Curry's logic D. Curry's logic D is an extension of minimal logic by the law of excluded middle and its Q-semantics was provided by Segerberg (1968). The relationship between Humberstone's logic and Curry's D was already studied by Niki & Omori (2021), where it was shown that Humberstone's logic and D have the same set of valid formulas but their semantic consequence relations are different. Based on these facts, we reveal in the Q-semantics for D a non-standard notion of a semantic consequence relation that exactly comprises a semantic consequence relation of Humberstone's logic. Consequently, we show that (i) can be alleviated and (ii) can be dropped. Moreover, we propose an informal interpretation of Humberstone's constant Ω by making use of the fact that Humberstone's logic can be regarded as an extension of minimal logic.
Katsuhiko Sano (Hokkaido University)
Title: Axiomatizing a Simple Logic of the Hide and Seek Game
Abstract: This talk provides a semantically complete axiomatization of a hybridization of a simple modal logic of the hide-and-seek game by Li et al. (2021). To describe the winning condition of the seeker of the game, the logic has an equality constant, which is similar to a diagonal constant introduced in the product of modal logics by Kurucz (2009). While the original simple modal logic of the hide-and-seek game was shown to be undecidable in Li et al. (2021), it is still open whether the logic has a semantically complete finite axiomatization. In this talk, we show that a hybridization (a hybrid logic expansion, in particular that for the product of modal logic, cf. Sano (2010)) provides an answer to the open question, provided that the syntax is expanded with nominals and satisfaction operators. If time permits, we also explain a recent progress on a finite axiomatization of a hybridization of modal logic with the diagonal constant, while the non-hybridized version was shown not to be finitely axiomatizable by Kikot (2010). This is a joint work with Dazhu Li (Chinese Academy of Sciences) and Fenrong Liu (Tsinghua).
Sara Ayhan (Ruhr University Bochum)
Title: Sense and denotation in systems for proofs and refutations
Abstract: In this talk I will consider questions about sense, reference, identity and synonymy of proofs and refutations in a setting of bilateralist proof-theoretic semantics. In this context there are two issues that will be addressed in this talk. Firstly, I want to give an account - building upon Frege’s famous distinction - on how it is possible to distinguish between sense and reference of derivations in a spirit of proof-theoretic semantics. While the question of reference and identity of proofs has received quite some attention, I will also give a conception of what constitutes the sense of derivations and thereby we will be able to make more fine-grained distinctions: not only can we give an answer to the question of when two derivations are identical but also to the question of when they must be considered synonymous.
Secondly, I will extend this to a bilateralist perspective and consider the relation between proofs and refutations in the context of such a Fregean distinction. Using my account about what constitutes sense and reference of derivations, I will show how this yields a (from a bilateralist point of view) desired balance between proofs and refutations: they are considered as equal; neither concept is reduced to the other and no preference is given to one or the other.
Hitoshi Omori (Tohoku University)
Title: Why Weak Kleene logic might matter for logic of agent
Abstract: For the purpose of developing logic of agent, the standard strategy is to make use of some kind of modal logic suitably tuned to deal with issues such as knowledge, belief, action, decision-making and more. These issues are highly complicated, and require highly non-trivial machinery. In this paper, however, we are interested in a far more simple scenario with agents attempting to communicate and understand each other in contexts involving use of several natural languages. We will present a semantic framework building on the work by Hans Herzberger, and observe how Weak Kleene logic, classical logic, and Paraconsistent Weak Kleene logic are related to each other. (This is a joint work with Jonas R. B. Arenhart.)
Organizer
Takuro Onishi (takuro.onishi@gmail.com), Shawn Standefer