•  117
    Hybrid counterfactual logics David Lewis meets Arthur prior again
    Journal of Logic, Language and Information 18 (4): 515-539. 2009.
    The purpose of this paper is to argue that the hybrid formalism fits naturally in the context of David Lewis’s counterfactual logic and that its introduction into this framework is desirable. This hybridization enables us to regard the inference “The pig is Mary; Mary is pregnant; therefore the pig is pregnant” as a process of updating local information (which depends on the given situation) by using global information (independent of the situation). Our hybridization also has the following tech…Read more
  •  55
    Generalizing Functional Completeness in Belnap-Dunn Logic
    Studia Logica 103 (5): 883-917. 2015.
    One of the problems we face in many-valued logic is the difficulty of capturing the intuitive meaning of the connectives introduced through truth tables. At the same time, however, some logics have nice ways to capture the intended meaning of connectives easily, such as four-valued logic studied by Belnap and Dunn. Inspired by Dunn’s discovery, we first describe a mechanical procedure, in expansions of Belnap-Dunn logic, to obtain truth conditions in terms of the behavior of the Truth and the Fa…Read more
  •  35
    Semantical Characterizations for Irreflexive and Generalized Modal Languages
    with Katsuhiko Sano and Kentaro Sato
    Notre Dame Journal of Formal Logic 48 (2): 205-228. 2007.
    This paper deals with two main topics: One is a semantical investigation for a bimodal language with a modal operator \blacksquare associated with the intersection of the accessibility relation R and the inequality ≠. The other is a generalization of some of the former results to general extended languages with modal operators. First, for our language L\sb{\square\blacksquare}, we prove that Segerberg's theorem (equivalence between finite frame property and finite model property) fails and estab…Read more
  •  22
    The Expressive Power of Modal Dependence Logic
    with Lauri Hella, Kerkko Luosto, and Jonni Virtema
    In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10, Csli Publications. pp. 294-312. 2014.
  •  22
    Recapturing Dynamic Logic of Relation Changers via Bounded Morphisms
    with Ryo Hatano
    Studia Logica 109 (1): 95-124. 2020.
    The present contribution shows that a Hilbert-style axiomatization for dynamic logic of relation changers is complete for the standard Kripke semantics not by a well-known rewriting technique but by the idea of an auxiliary semantics studied by van Benthem and Wang et al. A key insight of our auxiliary semantics for dynamic logic of relation changers can be described as: “relation changers are bounded morphisms.” Moreover, we demonstrate that this semantic insight can be used to provide a modula…Read more
  •  20
    Dynamic Epistemic Logic for Channel-Based Agent Communication
    with Satoshi Tojo
    In Kamal Lodaya (ed.), Logic and its Applications, Springer. pp. 109--120. 2013.
  •  16
    Characterising modal definability of team-based logics via the universal modality
    with Jonni Virtema
    Annals of Pure and Applied Logic 170 (9): 1100-1127. 2019.
  •  16
    Bimodal Logic with the Irreflxive Modality
    with Yasuo Nakayama
    Journal of the Japan Association for Philosophy of Science 34 (1): 1-10. 2007.
  •  16
    Dynamic epistemic logic of belief change in legal judgments
    with Pimolluck Jirakunkanok and Satoshi Tojo
    Artificial Intelligence and Law 26 (3): 201-249. 2018.
    This study realizes belief/reliability change of a judge in a legal judgment by dynamic epistemic logic. A key feature of DEL is that possibilities in an agent’s belief can be represented by a Kripke model. This study addresses two difficulties in applying DEL to a legal case. First, since there are several methods for constructing a Kripke model, our question is how we can construct the model from a legal case. Second, since this study employs several dynamic operators, our question is how we c…Read more
  •  15
    This paper studies a combined system of intuitionistic and classical propositional logic from proof-theoretic viewpoints. Based on the semantic treatment of Humberstone (J Philos Log 8:171–196, 1979) and del Cerro and Herzig (Frontiers of combining systems: FroCoS, Springer, 1996), a sequent calculus $$\textsf{G}(\textbf{C}+\textbf{J})$$ is proposed. An approximate idea of obtaining $$\textsf{G}(\textbf{C}+\textbf{J})$$ is adding rules for classical implication on top of the intuitionistic multi…Read more
  •  13
    Goldblatt-Thomason-style Theorems for Graded Modal Language
    with Minghui Ma
    In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 330-349. 1998.
  •  12
    Artemov and Protopopescu introduced a Brouwer-Heyting-Kolmogorov interpretation of knowledge operator to define the intuitionistic epistemic logic IEL, where the axiom A⊃KA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A\supset KA$$\end{document} is accepted but the axiom KA⊃A\documentclass[12pt]{minimal} \usepackag…Read more
  •  9
    Intuitionistic epistemic logic by Artemov and Protopopescu (Rev Symb Log 9:266–298, 2016) accepts the axiom “if A, then A is known” (written $$A \supset K A$$ ) in terms of the Brouwer–Heyting–Kolmogorov interpretation. There are two variants of intuitionistic epistemic logic: one with the axiom “ $$KA \supset \lnot \lnot A$$ ” and one without it. The former is called $$\textbf{IEL}$$, and the latter is called $$\textbf{IEL}^{-}$$. The aim of this paper is to study first-order expansions (with e…Read more
  •  8
    Semantic Incompleteness of Hilbert system for a Combination of Classical and Intuitionistic Propositional Logic
    with Masanobu Toyooka
    Australasian Journal of Logic 20 (3): 397-411. 2023.
    This paper shows Hilbert system (C+J)-, given by del Cerro and Herzig (1996) is semantically incomplete. This system is proposed as a proof theory for Kripke semantics for a combination of intuitionistic and classical propositional logic, which is obtained by adding the natural semantic clause of classical implication into intuitionistic Kripke semantics. Although Hilbert system (C+J)- contains intuitionistic modus ponens as a rule, it does not contain classical modus ponens. This paper gives an…Read more
  •  4
    We develop intuitionistic public announcement logic over intuitionistic \({\textbf{K}}\), \({{\textbf{K}}}{{\textbf{T}}}\), \({{\textbf{K}}}{{\textbf{4}}}\), and \({{\textbf{S}}}{{\textbf{4}}}\) with distributed knowledge. We reveal that a recursion axiom for the distributed knowledge is _not_ valid for a frame class discussed in [ 12 ] but valid for the restricted frame class introduced in [ 20, 26 ]. The semantic completeness of the static logics for this restricted frame class is established …Read more
  •  1
    正しいから証明できるのか、証明できるから正しいのか。数学にとって証明とは何か、正しさとは何なのかは数学基礎論の根本的な問題である。様相論理を軸とした、証明と真理に関わる数学基礎論の古典的な結果から最先端の議論までを解説した。