•  4
    Persons with visual impairments (hereafter PVI) detect and discover obstacles and road conditions by touching with a white cane when walking on the streets. In one training session, an Orientation and Mobility specialist (hereafter SPT) guided a PVI by grasping and moving the cane that the PVI was holding. We conducted a multimodal analysis of two instruction sequences, one a "proving and achieving" demonstration (Sacks in Lectures on conversation, Blackwell, 1992) and the other a "learnable" (Z…Read more
  •  23
    Wittgenstein on Equinumerosity and Surveyability
    Grazer Philosophische Studien 89 (1): 61-78. 2014.
  •  47
    The thesis according to which the meaning of a mathematical sentence is given by its proof was held by both Wittgenstein and the intuitionists, following Heyting and Dummett. In this paper, we clarify the meaning of this thesis for Wittgenstein, showing how his position differs from that of the intuitionists. We show how the thesis originates in his thoughts, from the middle period, about proofs by induction, and we sketch his answers to a number of objections, including the idea that, given the…Read more
  •  8
  •  3
    特集テーマ「タイプ理論」について
    Kagaku Tetsugaku 53 (2): 1. 2021.
  •  64
    The paper traces the development and the role of syntactic reduction in Edmund Husserl’s early writings on mathematics and logic, especially on arithmetic. The notion has its origin in Hermann Hankel’s principle of permanence that Husserl set out to clarify. In Husserl’s early texts the emphasis of the reductions was meant to guarantee the consistency of the extended algorithm. Around the turn of the century Husserl uses the same idea in his conception of definiteness of what he calls “mathemati…Read more
  • Following a Rule: Waismann's Variation
    In Gabriele M. Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics, De Gruyter. pp. 359-373. 2018.
  •  210
    We present some ideas on logical process descriptions, using relations from the DIO (Drug Interaction Ontology) as examples and explaining how these relations can be naturally decomposed in terms of more basic structured logical process descriptions using terms from linear logic. In our view, the process descriptions are able to clarify the usual relational descriptions of DIO. In particular, we discuss the use of logical process descriptions in proving linear logical theorems. Among the types o…Read more
  •  15
    A Direct Independence Proof of Buchholz's Hydra Game on Finite Labeled Trees
    with Masahiro Hamano
    Bulletin of Symbolic Logic 7 (4): 534-535. 2001.
  •  8
    A Proof-theoretic Study Of The Correspondence Of Classical Logic And Modal Logic
    with H. Kushida
    Journal of Symbolic Logic 68 (4): 1403-1414. 2003.
    It is well known that the modal logic S5 can be embedded in the classical predicate logic by interpreting the modal operator in terms of a quantifier. Wajsberg proved this fact in a syntactic way. Mints extended this result to the quantified version of S5; using a purely proof-theoretic method he showed that the quantified S5 corresponds to the classical predicate logic with one-sorted variable. In this paper we extend Mints’ result to the basic modal logic S4; we investigate the correspondence …Read more
  • Reasoning and Cognition (edited book)
    with D. Andler and I. Watanabe
    . 2006.
  •  34
    A proof–theoretic study of the correspondence of hybrid logic and classical logic
    with H. Kushida
    Journal of Logic, Language and Information 16 (1): 35-61. 2006.
    In this paper, we show the equivalence between the provability of a proof system of basic hybrid logic and that of translated formulas of the classical predicate logic with equality and explicit substitution by a purely proof–theoretic method. Then we show the equivalence of two groups of proof systems of hybrid logic: the group of labelled deduction systems and the group of modal logic-based systems.
  •  46
    A proof-theoretic study of the correspondence of classical logic and modal logic
    with H. Kushida
    Journal of Symbolic Logic 68 (4): 1403-1414. 2003.
    It is well known that the modal logic S5 can be embedded in the classical predicate logic by interpreting the modal operator in terms of a quantifier. Wajsberg [10] proved this fact in a syntactic way. Mints [7] extended this result to the quantified version of S5; using a purely proof-theoretic method he showed that the quantified S5 corresponds to the classical predicate logic with one-sorted variable. In this paper we extend Mints' result to the basic modal logic S4; we investigate the corres…Read more
  •  11
    A New Correctness Criterion For The Proof Nets Of Non-commutative Multiplicative Linear Logics
    with Misao Nagayama
    Journal of Symbolic Logic 66 (4): 1524-1542. 2001.
    This paper presents a new correctness criterion for marked Danos-Reginer graphs of Multiplicative Cyclic Linear Logic MCLL and Abrusci's non-commutative Linear Logic MNLL. As a corollary we obtain an affirmative answer to the open question whether a known quadratic-time algorithm for the correctness checking of proof nets for MCLL and MNLL can be improved to linear-time.
  •  74
    A Diagrammatic Inference System with Euler Circles
    with Koji Mineshima and Ryo Takemura
    Journal of Logic, Language and Information 21 (3): 365-391. 2012.
    Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by logicians. Euler diagrams were introduced in the eighteenth century. But it is quite recent (more precisely, in the 1990s) that logicians started to study them from a formal logical viewpoint. We propose a novel approach to the formalization of Euler diagrammatic reasoning, …Read more
  •  21
    Genetic Factors of Individual Differences in Decision Making in Economic Behavior: A Japanese Twin Study using the Allais Problem
    with Chizuru Shikishima, Kai Hiraishi, Shinji Yamagata, and Juko Ando
    Frontiers in Psychology 6. 2015.
  •  67
    The finite model property for various fragments of intuitionistic linear logic
    with Kazushige Terui
    Journal of Symbolic Logic 64 (2): 790-802. 1999.
    Recently Lafont [6] showed the finite model property for the multiplicative additive fragment of linear logic (MALL) and for affine logic (LLW), i.e., linear logic with weakening. In this paper, we shall prove the finite model property for intuitionistic versions of those, i.e. intuitionistic MALL (which we call IMALL), and intuitionistic LLW (which we call ILLW). In addition, we shall show the finite model property for contractive linear logic (LLC), i.e., linear logic with contraction, and for…Read more
  •  57
    A Generalized Syllogistic Inference System based on Inclusion and Exclusion Relations
    with Koji Mineshima and Ryo Takemura
    Studia Logica 100 (4): 753-785. 2012.
    We introduce a simple inference system based on two primitive relations between terms, namely, inclusion and exclusion relations. We present a normalization theorem, and then provide a characterization of the structure of normal proofs. Based on this, inferences in a syllogistic fragment of natural language are reconstructed within our system. We also show that our system can be embedded into a fragment of propositional minimal logic
  •  39
    We introduce subsystems WLJ and SI of the intuitionistic propositional logic LJ, by weakening the intuitionistic implication. These systems are justifiable by purely constructive semantics. Then the intuitionistic implication with full strength is definable in the second order versions of these systems. We give a relationship between SI and a weak modal system WM. In Appendix the Kripke-type model theory for WM is given.
  •  45
    A direct independence proof of Buchholz's Hydra Game on finite labeled trees
    with Masahiro Hamano
    Archive for Mathematical Logic 37 (2): 67-89. 1998.
    We shall give a direct proof of the independence result of a Buchholz style-Hydra Game on labeled finite trees. We shall show that Takeuti-Arai's cut-elimination procedure of $(\Pi^{1}_{1}-CA) + BI$ and of the iterated inductive definition systems can be directly expressed by the reduction rules of Buchholz's Hydra Game. As a direct corollary the independence result of the Hydra Game follows.
  •  15
    The Finite Model Property for Various Fragments of Intuitionistic Linear Logic
    with Kazushige Terui
    Journal of Symbolic Logic 64 (2): 790-802. 1999.
    Recently Lafont [6] showed the finite model property for the multiplicative additive fragment of linear logic and for affine logic, i.e., linear logic with weakening. In this paper, we shall prove the finite model property for intuitionistic versions of those, i.e. intuitionistic MALL, and intuitionistic LLW. In addition, we shall show the finite model property for contractive linear logic, i.e., linear logic with contraction, and for its intuitionistic version. The finite model property for rel…Read more
  •  39
    A new correctness criterion for the proof nets of non-commutative multiplicative linear logics
    with Misao Nagayama
    Journal of Symbolic Logic 66 (4): 1524-1542. 2001.
    This paper presents a new correctness criterion for marked Danos-Reginer graphs (D-R graphs, for short) of Multiplicative Cyclic Linear Logic MCLL and Abrusci's non-commutative Linear Logic MNLL. As a corollary we obtain an affirmative answer to the open question whether a known quadratic-time algorithm for the correctness checking of proof nets for MCLL and MNLL can be improved to linear-time