17 found
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  1.  66
    Conjunction and Disjunction in Infectious Logics.Hitoshi Omori & Damian Szmuc - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction: 6th International Workshop. Berlin: Springer. pp. 268-283.
    In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that none of them discusses (...)
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  2.  32
    Classical Negation and Expansions of Belnap–Dunn Logic.Michael De & Hitoshi Omori - 2015 - Studia Logica 103 (4):825-851.
    We investigate the notion of classical negation from a non-classical perspective. In particular, one aim is to determine what classical negation amounts to in a paracomplete and paraconsistent four-valued setting. We first give a general semantic characterization of classical negation and then consider an axiomatic expansion BD+ of four-valued Belnap–Dunn logic by classical negation. We show the expansion complete and maximal. Finally, we compare BD+ to some related systems found in the literature, specifically a four-valued modal logic of Béziau and (...)
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  3.  14
    Generalizing Functional Completeness in Belnap-Dunn Logic.Hitoshi Omori & Katsuhiko Sano - 2015 - Studia Logica 103 (5):883-917.
    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 False, (...)
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  4. Some New Results on PCL1 and its Related Systems.Toshiharu Waragai & Hitoshi Omori - 2010 - Logic and Logical Philosophy 19 (1-2):129-158.
    In [Waragai & Shidori, 2007], a system of paraconsistent logic called PCL1, which takes a similar approach to that of da Costa, is proposed. The present paper gives further results on this system and its related systems. Those results include the concrete condition to enrich the system PCL1 with the classical negation, a comparison of the concrete notion of “behaving classically” given by da Costa and by Waragai and Shidori, and a characterisation of the notion of “behaving classically” given by (...)
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  5.  18
    40 Years of FDE: An Introductory Overview.Hitoshi Omori & Heinrich Wansing - 2017 - Studia Logica 105 (6):1021-1049.
    In this introduction to the special issue “40 years of FDE”, we offer an overview of the field and put the papers included in the special issue into perspective. More specifically, we first present various semantics and proof systems for FDE, and then survey some expansions of FDE by adding various operators starting with constants. We then turn to unary and binary connectives, which are classified in a systematic manner. First-order FDE is also briefly revisited, and we conclude by listing (...)
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  6.  3
    On Contra-Classical Variants of Nelson Logic N4 and its Classical Extension.Hitoshi Omori & Heinrich Wansing - forthcoming - Review of Symbolic Logic:1-16.
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  7.  12
    Remarks on Naive Set Theory Based on Lp.Hitoshi Omori - 2015 - Review of Symbolic Logic 8 (2):279-295.
  8.  22
    More on Empirical Negation.Michael De & Hitoshi Omori - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 114-133.
    Intuitionism can be seen as a verificationism restricted to mathematical discourse. An attempt to generalize intuitionism to empirical discourse presents various challenges. One of those concerns the logical and semantical behavior of what has been called ' empirical negation'. An extension of intuitionistic logic with empirical negation was given by Michael De and a labelled tableaux system was there shown sound and complete. However, a Hilbert-style axiom system that is sound and complete was missing. In this paper we provide the (...)
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  9.  9
    Observations on the Trivial World.Zach Weber & Hitoshi Omori - forthcoming - Erkenntnis:1-20.
    A world is trivial if it makes every proposition true all at once. Such a world is impossible, an absurdity. Our world, we hope, is not an absurdity. It is important, nevertheless, for semantic and metaphysical theories that we be able to reason cogently about absurdities—if only to see that they are absurd. In this note we describe methods for ‘observing’ absurd objects like the trivial world without falling in to incoherence, using some basic techniques from modal logic. The goal (...)
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  10.  3
    A Note on Goddard and Routley's Significance Logic.Damian Szmuc & Hitoshi Omori - 2018 - Australasian Journal of Logic 15 (2):431-448.
    The present note revisits the joint work of Leonard Goddard and Richard Routley on significance logics with the aim of shedding new light on their understanding by studying them under the lens of recent semantic developments, such as the plurivalent semantics developed by Graham Priest. These semantics allow sentences to receive one, more than one, or no truth-value at all from a given carrier set. Since nonsignificant sentences are taken to be neither true nor false, i.e. truth-value gaps, in this (...)
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  11.  33
    There is More to Negation Than Modality.Michael De & Hitoshi Omori - 2018 - Journal of Philosophical Logic 47 (2):281-299.
    There is a relatively recent trend in treating negation as a modal operator. One such reason is that doing so provides a uniform semantics for the negations of a wide variety of logics and arguably speaks to a longstanding challenge of Quine put to non-classical logics. One might be tempted to draw the conclusion that negation is a modal operator, a claim Francesco Berto, 761–793, 2015) defends at length in a recent paper. According to one such modal account, the negation (...)
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  12.  5
    A System of Paraconsistent Logic Equipped with Classical Negation.Toshiharu Waragai & Hitoshi Omori - 2009 - Journal of the Japan Association for Philosophy of Science 36 (1):9-18.
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  13.  5
    Axiomatizing Jaśkowski’s Discussive Logic $$Mathbf {D_2}$$.Hitoshi Omori & Jesse Alama - forthcoming - Studia Logica:1-18.
    We outline the rather complicated history of attempts at axiomatizing Jaśkowski’s discussive logic \ and show that some clarity can be had by paying close attention to the language we work with. We then examine the problem of axiomatizing \ in languages involving discussive conjunctions. Specifically, we show that recent attempts by Ciuciura are mistaken. Finally, we present an axiomatization of \ in the language Jaśkowski suggested in his second paper on discussive logic, by following a remark of da Costa (...)
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  14.  31
    On Béziau’s Logic Z.Hitoshi Omori & Toshiharu Waragai - 2008 - Logic and Logical Philosophy 17 (4):305-320.
    In [1] Béziau developed the paraconsistent logic Z, which is definitionally equivalent to the modal logic S5, and gave an axiomatization of the logic Z: the system HZ. In the present paper, we prove that some axioms of HZ are not independent and then propose another axiomatization of Z. We also discuss a new perspective on the relation between S5 and classical propositional logic with the help of the new axiomatization of Z. Then we conclude the paper by making a (...)
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  15.  2
    Classical and Empirical Negation in Subintuitionistic Logic.Michael De & Hitoshi Omori - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 217-235.
    Subintuitionistic (propositional) logics are those in a standard intuitionistic language that result by weakening the frame conditions of the Kripke semantics for intuitionistic logic. In this paper we consider two negation expansions of subintuitionistic logic, one by classical negation and the other by what has been dubbed “empirical” negation. We provide an axiomatization of each expansion and show them sound and strongly complete. We conclude with some final remarks, including avenues for future research.
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  16.  16
    A Note on Majkić's Systems.Hitoshi Omori & Toshiharu Waragai - 2010 - Notre Dame Journal of Formal Logic 51 (4):503-506.
    The present note offers a proof that systems developed by Majkić are actually extensions of intuitionistic logic, and therefore not paraconsistent.
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  17.  2
    On Extensions of a System of Paraconsistent Logic PCL1.Hitoshi Omori & Toshiharu Waragai - 2012 - Journal of the Japan Association for Philosophy of Science 39 (2):51-68.
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