32 found
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  1.  62
    Connexive logics. An overview and current trends.Hitoshi Omori & Heinrich Wansing - forthcoming - Logic and Logical Philosophy:1.
    In this introduction, we offer an overview of main systems developed in the growing literature on connexive logic, and also point to a few topics that seem to be collecting attention of many of those interested in connexive logic. We will also make clear the context to which the papers in this special issue belong and contribute.
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  2.  48
    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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  3.  20
    New Essays on Belnap-­Dunn Logic.Hitoshi Omori & Heinrich Wansing (eds.) - 2019 - Cham, Switzerland: Springer Verlag.
    This edited volume collects essays on the four-valued logic known as Belnap-Dunn logic, or first-degree entailment logic. It also looks at various formal systems closely related to it. These include the strong Kleene logic and the Logic of Paradox. Inside, readers will find reprints of seminal papers written by the fathers of the field: Nuel Belnap and Michael Dunn. In addition, the collection also features a well-known but previously unpublished manuscript of Dunn, an interview with Belnap, and a new essay (...)
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  4. Conjunction and Disjunction in Infectious Logics.Hitoshi Omori & Damian Szmuc - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan). 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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  5.  9
    A Note on “A Connexive Conditional”.Heinrich Wansing & Hitoshi Omori - 2022 - Logos and Episteme 13 (3):325-328.
    In a recent article, Mario Günther presented a conditional that is claimed to be connexive. The aim of this short discussion note is to show that Günther’s claim is not without problems.
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  6.  82
    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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  7.  53
    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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  8.  62
    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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  9.  47
    On contra-classical variants of Nelson logic n4 and its classical extension.Hitoshi Omori & Heinrich Wansing - 2018 - Review of Symbolic Logic 11 (4):805-820.
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  10.  45
    Remarks on naive set theory based on lp.Hitoshi Omori - 2015 - Review of Symbolic Logic 8 (2):279-295.
    Dialetheism is the metaphysical claim that there are true contradictions. And based on this view, Graham Priest and his collaborators have been suggesting solutions to a number of paradoxes. Those paradoxes include Russell’s paradox in naive set theory. For the purpose of dealing with this paradox, Priest is known to have argued against the presence of classical negation in the underlying logic of naive set theory. The aim of the present paper is to challenge this view by showing that there (...)
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  11.  28
    Shrieking, Shrugging, and the Australian Plan.Hitoshi Omori & Michael De - 2022 - Notre Dame Journal of Formal Logic 63 (2).
    We observe that Jc Beall’s shrieking and shrugging strategy gives us an opportunity to reflect on the Australian plan for negation in FDE, a basic subclassical logic that is used in Beall’s argument for subclassical logics. An implication of our observation is applied to a recent defense of the Australian plan for negation by Francesco Berto and Greg Restall.
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  12.  35
    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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  13.  19
    Change of logic, without change of meaning.Hitoshi Omori & Jonas R. B. Arenhart - 2023 - Theoria 89 (4):414-431.
    Change of logic is typically taken as requiring that the meanings of the connectives change too. As a result, it has been argued that legitimate rivalry between logics is under threat. This is, in a nutshell, the meaning‐variance argument, traditionally attributed to Quine. In this paper, we present a semantic framework that allows us to resist the meaning‐variance claim for an important class of systems: classical logic, the logic of paradox and strong Kleene logic. The major feature of the semantics (...)
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  14.  27
    On Woodruff’s Constructive Nonsense Logic.Jonas R. B. Arenhart & Hitoshi Omori - forthcoming - Studia Logica:1-20.
    Sören Halldén’s logic of nonsense is one of the most well-known many-valued logics available in the literature. In this paper, we discuss Peter Woodruff’s as yet rather unexplored attempt to advance a version of such a logic built on the top of a constructive logical basis. We start by recalling the basics of Woodruff’s system and by bringing to light some of its notable features. We then go on to elaborate on some of the difficulties attached to it; on our (...)
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  15.  35
    Axiomatizing Jaśkowski’s Discussive Logic $$\mathbf {D_2}$$ D 2.Hitoshi Omori & Jesse Alama - 2018 - Studia Logica 106 (6):1163-1180.
    We outline the rather complicated history of attempts at axiomatizing Jaśkowski’s discussive logic $$\mathbf {D_2}$$ D2 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 $$\mathbf {D_2}$$ D2 in languages involving discussive conjunctions. Specifically, we show that recent attempts by Ciuciura are mistaken. Finally, we present an axiomatization of $$\mathbf {D_2}$$ D2 in the language Jaśkowski suggested in his second paper on discussive logic, by (...)
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  16.  52
    Observations on the Trivial World.Zach Weber & Hitoshi Omori - 2019 - Erkenntnis 84 (5):975-994.
    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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  17.  6
    A Generalization of Ordered-Pair Semantics.Hitoshi Omori & Jonas R. B. Arenhart - 2021 - In Sujata Ghosh & Thomas Icard (eds.), Logic, Rationality, and Interaction: 8th International Workshop, Lori 2021, Xi’an, China, October 16–18, 2021, Proceedings. Springer Verlag. pp. 149-157.
    In this paper, we generalize the ordered-pair semantics advanced by Matthew Clemens for the Logic of Paradox to n-tuple semantics, for each fixed n. Moreover, we show that the resulting semantics can accommodate not only LP, but also classical logic as well as strong Kleene logic depending on the set of designated values that one chooses. Building on the technical observations, we offer intuitively plausible readings for the semantics, and we also discuss some weaknesses of the original intuitive reading advanced (...)
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  18.  53
    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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  19.  9
    Connexive Logic, Connexivity, and Connexivism: Remarks on Terminology.Heinrich Wansing & Hitoshi Omori - forthcoming - Studia Logica:1-35.
    Over the past ten years, the community researching connexive logics is rapidly growing and a number of papers have been published. However, when it comes to the terminology used in connexive logic, it seems to be not without problems. In this introduction, we aim at making a contribution towards both unifying and reducing the terminology. We hope that this can help making it easier to survey and access the field from outside the community of connexive logicians. Along the way, we (...)
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  20.  6
    A Generalization of Beall’s Off-Topic Interpretation.Yang Song, Hitoshi Omori, Jonas R. B. Arenhart & Satoshi Tojo - forthcoming - Studia Logica:1-40.
    In one of his papers, JC Beall advanced a new and interesting interpretation of Weak Kleene logic, in terms of on-topic/off-topic. In brief, Beall suggests to read the third value as off-topic, whereas the two classical values are read as true and on-topic and false and on-topic. Building on Beall’s new interpretation, the aim of this paper is threefold. First, we discuss two motivations to enrich Beall’s interpretation, and offer an alternative semantic framework that reflects our motivations. Second, by making (...)
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  21. Liberating classical negation from falsity conditions.Damian Szmuc & Hitoshi Omori - 2022 - Proceedings of the 52nd International Symposium on Multiple-Valued Logic (ISMVL 2022).
    In one of their papers, Michael De and Hitoshi Omori observed that the notion of classical negation is not uniquely determined in the context of so-called Belnap-Dunn logic, and in fact there are 16 unary operations that qualify to be called classical negation. These varieties are due to different falsity conditions one may assume for classical negation. The aim of this paper is to observe that there is an interesting way to make sense of classical negation independent of falsity conditions. (...)
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  22.  5
    Why FDE might be too strong for Beall.Jonas R. B. Arenhart & Hitoshi Omori - 2024 - Asian Journal of Philosophy 3 (1):1-16.
    In his “The simple argument for subclassical logic,” Jc Beall advances an argument that led him to take FDE as the one true logic (the latter point is explicitly made clear in his “FDE as the One True Logic”). The aim of this article is to point out that if we follow Beall’s line of reasoning for endorsing FDE, there are at least two additional reasons to consider that FDE is too strong for Beall’s purposes. In fact, we claim that (...)
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  23.  31
    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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  24. 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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  25.  29
    Knot much like tonk.Michael De & Hitoshi Omori - 2022 - Synthese 200 (149):1-14.
    Connectives such as Tonk have posed a significant challenge to the inferentialist. It has been recently argued that the classical semanticist faces an analogous problem due to the definability of “nasty connectives” under non-standard interpretations of the classical propositional vocabulary. In this paper, we defend the classical semanticist from this alleged problem.
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  26.  94
    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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  27.  2
    Angell and McCall Meet Wansing.Hitoshi Omori & Andreas Kapsner - forthcoming - Studia Logica:1-25.
    In this paper, we introduce a new logic, which we call AM3. It is a connexive logic that has several interesting properties, among them being strongly connexive and validating the Converse Boethius Thesis. These two properties are rather characteristic of the difference between, on the one hand, Angell and McCall’s CC1 and, on the other, Wansing’s C. We will show that in other aspects, as well, AM3 combines what are, arguably, the strengths of both CC1 and C. It also allows (...)
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  28.  34
    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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  29.  6
    A Note on Ciuciura’s mbC1.Hitoshi Omori - 2019 - Bulletin of the Section of Logic 48 (3):161-171.
    This note offers a non-deterministic semantics for mbC1, introduced by Janusz Ciuciura, and establishes soundness and completeness results with respect to the Hilbert-style proof system. Moreover, based on the new semantics, we briefly discuss an unexplored variant of mbC1 which has a contra-classical flavor.
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  30.  15
    From logics of formal inconsistency to logics of formal classicality.Hitoshi Omori - 2020 - Logic Journal of the IGPL 28 (5):684-711.
    One of the oldest systems of paraconsistent logic is the set of so-called C-systems of Newton da Costa, and this has been generalized into a family of systems now known as logics of formal inconsistencies by Walter Carnielli, Marcelo Coniglio and João Marcos. The characteristic notion in these systems is the so-called consistency operator which, roughly speaking, indicates how gluts are behaving. One natural question then is to ask if we can let not only gluts but also gaps be around (...)
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  31.  5
    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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  32.  15
    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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