133 found
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  1.  69
    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.  64
    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. Remarks on the logic of imagination. A step towards understanding doxastic control through imagination.Heinrich Wansing - 2017 - Synthese 194 (8):2843-2861.
    Imagination has recently attracted considerable attention from epistemologists and is recognized as a source of belief and even knowledge. One remarkable feature of imagination is that it is often and typically agentive: agents decide to imagine. In cases in which imagination results in a belief, the agentiveness of imagination may be taken to give rise to indirect doxastic control and epistemic responsibility. This observation calls for a proper understanding of agentive imagination. In particular, it calls for the development of a (...)
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  4.  28
    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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  5.  20
    Truth and Falsehood: An Inquiry Into Generalized Logical Values.Yaroslav Shramko & Heinrich Wansing - 2011 - Dordrecht, Netherland: Springer.
    The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...)
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  6. Some Useful 16-Valued Logics: How a Computer Network Should Think.Yaroslav Shramko & Heinrich Wansing - 2005 - Journal of Philosophical Logic 34 (2):121-153.
    In Belnap's useful 4-valued logic, the set 2 = {T, F} of classical truth values is generalized to the set 4 = ������(2) = {Ø, {T}, {F}, {T, F}}. In the present paper, we argue in favor of extending this process to the set 16 = ᵍ (4) (and beyond). It turns out that this generalization is well-motivated and leads from the bilattice FOUR₂ with an information and a truth-and-falsity ordering to another algebraic structure, namely the trilattice SIXTEEN₃ with an (...)
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  7.  8
    Displaying Modal Logic.Heinrich Wansing - 1998 - Dordrecht, Netherland: Springer.
    The present monograph is a slightly revised version of my Habilitations schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen's sequent calculus developed by Nuel D. Belnap. This book is far from offering a comprehensive presentation of generalized sequent systems for modal logics broadly conceived. (...)
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  8.  44
    Connexive logic.Heinrich Wansing - 2008 - Stanford Encyclopedia of Philosophy.
  9.  64
    One Heresy and One Orthodoxy: On Dialetheism, Dimathematism, and the Non-normativity of Logic.Heinrich Wansing - 2024 - Erkenntnis 89 (1):181-205.
    In this paper, Graham Priest’s understanding of dialetheism, the view that there exist true contradictions, is discussed, and various kinds of metaphysical dialetheism are distinguished between. An alternative to dialetheism is presented, namely a thesis called ‘dimathematism’. It is pointed out that dimathematism enables one to escape a slippery slope argument for dialetheism that has been put forward by Priest. Moreover, dimathematism is presented as a thesis that is helpful in rejecting the claim that logic is a normative discipline.
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  10.  40
    Negation as Cancellation, Connexive Logic, and qLPm.Heinrich Wansing - 2018 - Australasian Journal of Logic 15 (2):476-488.
    In this paper, we shall consider the so-called cancellation view of negation and the inferential role of contradictions. We will discuss some of the problematic aspects of negation as cancellation, such as its original presentation by Richard and Valery Routley and its role in motivating connexive logic. Furthermore, we will show that the idea of inferential ineffectiveness of contradictions can be conceptually separated from the cancellation model of negation by developing a system we call qLPm, a combination of Graham Priest’s (...)
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  11.  35
    Logical Multilateralism.Heinrich Wansing & Sara Ayhan - 2023 - Journal of Philosophical Logic 52 (6):1603-1636.
    In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with (...)
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  12.  15
    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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  13.  20
    A more general general proof theory.Heinrich Wansing - 2017 - Journal of Applied Logic 25:23-46.
  14.  91
    Constructive negation, implication, and co-implication.Heinrich Wansing - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):341-364.
    In this paper, a family of paraconsistent propositional logics with constructive negation, constructive implication, and constructive co-implication is introduced. Although some fragments of these logics are known from the literature and although these logics emerge quite naturally, it seems that none of them has been considered so far. A relational possible worlds semantics as well as sound and complete display sequent calculi for the logics under consideration are presented.
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  15.  76
    Routley Star and Hyperintensionality.Sergei Odintsov & Heinrich Wansing - 2020 - Journal of Philosophical Logic 50 (1):33-56.
    We compare the logic HYPE recently suggested by H. Leitgeb as a basic propositional logic to deal with hyperintensional contexts and Heyting-Ockham logic introduced in the course of studying logical aspects of the well-founded semantics for logic programs with negation. The semantics of Heyting-Ockham logic makes use of the so-called Routley star negation. It is shown how the Routley star negation can be obtained from Dimiter Vakarelov’s theory of negation and that propositional HYPE coincides with the logic characterized by the (...)
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  16.  51
    Modal logics with Belnapian truth values.Serge P. Odintsov & Heinrich Wansing - 2010 - Journal of Applied Non-Classical Logics 20 (3):279-304.
    Various four- and three-valued modal propositional logics are studied. The basic systems are modal extensions BK and BS4 of Belnap and Dunn's four-valued logic of firstdegree entailment. Three-valued extensions of BK and BS4 are considered as well. These logics are introduced semantically by means of relational models with two distinct evaluation relations, one for verification and the other for falsification. Axiom systems are defined and shown to be sound and complete with respect to the relational semantics and with respect to (...)
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  17.  43
    Disentangling FDE -Based Paraconsistent Modal Logics.Sergei P. Odintsov & Heinrich Wansing - 2017 - Studia Logica 105 (6):1221-1254.
    The relationships between various modal logics based on Belnap and Dunn’s paraconsistent four-valued logic FDE are investigated. It is shown that the paraconsistent modal logic \, which lacks a primitive possibility operator \, is definitionally equivalent with the logic \, which has both \ and \ as primitive modalities. Next, a tableau calculus for the paraconsistent modal logic KN4 introduced by L. Goble is defined and used to show that KN4 is definitionally equivalent with \ without the absurdity constant. Moreover, (...)
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  18.  16
    Negation.Heinrich Wansing - 2017 - In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Oxford, UK: Blackwell. pp. 415–436.
    This chapter is concerned with logical aspects of negation, i.e. with the role of negation in valid inferences and hence with the contribution negation makes to the truth and falsity conditions of declarative expressions. Negation is an important philosophical and logical concept. Often differences between logical systems can ‐ at least partially ‐ be described as differences between the notions of negation used in these logics.
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  19. Displaying Modal Logic.Heinrich Wansing - 2000 - Studia Logica 66 (3):421-426.
  20.  97
    A general possible worlds framework for reasoning about knowledge and belief.Heinrich Wansing - 1990 - Studia Logica 49 (4):523 - 539.
    In this paper non-normal worlds semantics is presented as a basic, general, and unifying approach to epistemic logic. The semantical framework of non-normal worlds is compared to the model theories of several logics for knowledge and belief that were recently developed in Artificial Intelligence (AI). It is shown that every model for implicit and explicit belief (Levesque), for awareness, general awareness, and local reasoning (Fagin and Halpern), and for awareness and principles (van der Hoek and Meyer) induces a non-normal worlds (...)
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  21.  61
    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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  22.  11
    A Note on Synonymy in Proof-Theoretic Semantics.Heinrich Wansing - 2024 - In Thomas Piecha & Kai F. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics. Springer. pp. 339-362.
    The topic of identity of proofs was put on the agenda of general (or structural) proof theory at an early stage. The relevant question is: When are the differences between two distinct proofs (understood as linguistic entities, proof figures) of one and the same formula so inessential that it is justified to identify the two proofs? The paper addresses another question: When are the differences between two distinct formulas so inessential that these formulas admit of identical proofs? The question appears (...)
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  23.  38
    The Logic of Generalized Truth Values and the Logic of Bilattices.Sergei P. Odintsov & Heinrich Wansing - 2015 - Studia Logica 103 (1):91-112.
    This paper sheds light on the relationship between the logic of generalized truth values and the logic of bilattices. It suggests a definite solution to the problem of axiomatizing the truth and falsity consequence relations, \ and \ , considered in a language without implication and determined via the truth and falsity orderings on the trilattice SIXTEEN 3 . The solution is based on the fact that a certain algebra isomorphic to SIXTEEN 3 generates the variety of commutative and distributive (...)
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  24.  46
    An Axiomatic System and a Tableau Calculus for STIT Imagination Logic.Grigory K. Olkhovikov & Heinrich Wansing - 2018 - Journal of Philosophical Logic 47 (2):259-279.
    We formulate a Hilbert-style axiomatic system and a tableau calculus for the STIT-based logic of imagination recently proposed in Wansing. Completeness of the axiom system is shown by the method of canonical models; completeness of the tableau system is also shown by using standard methods.
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  25. Hyper-contradictions, generalized truth values and logics of truth and falsehood.Yaroslav Shramko & Heinrich Wansing - 2006 - Journal of Logic, Language and Information 15 (4):403-424.
    In Philosophical Logic, the Liar Paradox has been used to motivate the introduction of both truth value gaps and truth value gluts. Moreover, in the light of “revenge Liar” arguments, also higher-order combinations of generalized truth values have been suggested to account for so-called hyper-contradictions. In the present paper, Graham Priest's treatment of generalized truth values is scrutinized and compared with another strategy of generalizing the set of classical truth values and defining an entailment relation on the resulting sets of (...)
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  26.  20
    On Synonymy in Proof-Theoretic Semantics: The Case of \(\mathtt{2Int}\).Sara Ayhan & Heinrich Wansing - 2023 - Bulletin of the Section of Logic 52 (2):187-237.
    We consider an approach to propositional synonymy in proof-theoretic semantics that is defined with respect to a bilateral G3-style sequent calculus \(\mathtt{SC2Int}\) for the bi-intuitionistic logic \(\mathtt{2Int}\). A distinctive feature of \(\mathtt{SC2Int}\) is that it makes use of two kind of sequents, one representing proofs, the other representing refutations. The structural rules of \(\mathtt{SC2Int}\), in particular its cut rules, are shown to be admissible. Next, interaction rules are defined that allow transitions from proofs to refutations, and vice versa, mediated through (...)
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  27.  86
    Diamonds are a philosopher's best friends.Heinrich Wansing - 2002 - Journal of Philosophical Logic 31 (6):591-612.
    The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is (...)
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  28.  89
    The Idea of a Proof-Theoretic Semantics and the Meaning of the Logical Operations.Heinrich Wansing - 2000 - Studia Logica 64 (1):3-20.
    This is a purely conceptual paper. It aims at presenting and putting into perspective the idea of a proof-theoretic semantics of the logical operations. The first section briefly surveys various semantic paradigms, and Section 2 focuses on one particular paradigm, namely the proof-theoretic semantics of the logical operations.
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  29.  99
    Suszko’s Thesis, Inferential Many-valuedness, and the Notion of a Logical System.Heinrich Wansing & Yaroslav Shramko - 2008 - Studia Logica 88 (3):405-429.
    According to Suszko’s Thesis, there are but two logical values, true and false. In this paper, R. Suszko’s, G. Malinowski’s, and M. Tsuji’s analyses of logical twovaluedness are critically discussed. Another analysis is presented, which favors a notion of a logical system as encompassing possibly more than one consequence relation. [A] fundamental problem concerning many-valuedness is to know what it really is. [13, p. 281].
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  30.  40
    Inference as Doxastic Agency. Part I: The Basics of Justification Stit Logic.Grigory K. Olkhovikov & Heinrich Wansing - 2019 - Studia Logica 107 (1):167-194.
    In this paper we consider logical inference as an activity that results in proofs and hence produces knowledge. We suggest to merge the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. The general idea is to understand proving that A as seeing to it that a proof of A is available. We introduce a semantics of various notions of proving as an activity and present a number of valid principles that (...)
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  31. On Split Negation, Strong Negation, Information, Falsification, and Verification.Heinrich Wansing - 2016 - In Katalin Bimbó (ed.), J. Michael Dunn on Information Based Logics. Cham, Switzerland: Springer.
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  32.  48
    Connexive Conditional Logic. Part I.Heinrich Wansing & Matthias Unterhuber - forthcoming - Logic and Logical Philosophy:1.
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  33.  57
    Stit -logic for imagination episodes with voluntary input.Christopher Badura & Heinrich Wansing - 2023 - Review of Symbolic Logic 16 (3):813-861.
    Francesco Berto proposed a logic for imaginative episodes. The logic establishes certain (in)validities concerning episodic imagination. They are not all equally plausible as principles of episodic imagination. The logic also does not model that the initial input of an imaginative episode is deliberately chosen.Stit-imagination logic models the imagining agent’s deliberate choice of the content of their imagining. However, the logic does not model the episodic nature of imagination. The present paper combines the two logics, thereby modelling imaginative episodes with deliberately (...)
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  34.  69
    External Curries.Heinrich Wansing & Graham Priest - 2015 - Journal of Philosophical Logic 44 (4):453-471.
    Curry’s paradox is well known. The original version employed a conditional connective, and is not forthcoming if the conditional does not satisfy contraction. A newer version uses a validity predicate, instead of a conditional, and is not forthcoming if validity does not satisfy structural contraction. But there is a variation of the paradox which uses “external validity”. And since external validity contracts, one might expect the appropriate version of the Curry paradox to be inescapable. In this paper we show that (...)
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  35.  15
    Connexive Variants of Modal Logics Over FDE.Sergei Odintsov, Daniel Skurt & Heinrich Wansing - 2021 - In Ofer Arieli & Anna Zamansky (eds.), Arnon Avron on Semantics and Proof Theory of Non-Classical Logics. Springer Verlag. pp. 295-318.
    Various connexive FDE-based modal logics are studied. Some of these logics contain a conditional that is both connexive and strict, thereby highlighting that strictness and connexivity of a conditional do not exclude each other. In particular, the connexive modal logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, cKN4, scBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, scKN4, cMBL, and scMBL are introduced semantically by means of classes of Kripke models. The logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...)
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  36. What Is Negation?Dov M. Gabbay & Heinrich Wansing - 1999 - Studia Logica 69 (3):435-439.
  37.  31
    Hypersequent and Display Calculi – a Unified Perspective.Agata Ciabattoni, Revantha Ramanayake & Heinrich Wansing - 2014 - Studia Logica 102 (6):1245-1294.
    This paper presents an overview of the methods of hypersequents and display sequents in the proof theory of non-classical logics. In contrast with existing surveys dedicated to hypersequent calculi or to display calculi, our aim is to provide a unified perspective on these two formalisms highlighting their differences and similarities and discussing applications and recent results connecting and comparing them.
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  38.  11
    Negation: a notion in focus.Heinrich Wansing (ed.) - 1996 - New York: W. de Gruyter.
  39.  42
    Kripke Completeness of Bi-intuitionistic Multilattice Logic and its Connexive Variant.Norihiro Kamide, Yaroslav Shramko & Heinrich Wansing - 2017 - Studia Logica 105 (6):1193-1219.
    In this paper, bi-intuitionistic multilattice logic, which is a combination of multilattice logic and the bi-intuitionistic logic also known as Heyting–Brouwer logic, is introduced as a Gentzen-type sequent calculus. A Kripke semantics is developed for this logic, and the completeness theorem with respect to this semantics is proved via theorems for embedding this logic into bi-intuitionistic logic. The logic proposed is an extension of first-degree entailment logic and can be regarded as a bi-intuitionistic variant of the original classical multilattice logic (...)
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  40.  19
    Simplified Tableaux for STIT Imagination Logic.Grigory K. Olkhovikov & Heinrich Wansing - 2019 - Journal of Philosophical Logic 48 (6):981-1001.
    We show how to correct the analytic tableaux system from the paper Olkhovikov and Wansing, 259–279, 2018).
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  41.  11
    What is Negation?Dov M. Gabbay & Heinrich Wansing (eds.) - 1999 - Dordrecht, Netherland: Springer.
    The properties of negation, in combination with those of other logical operations and structural features of the deductibility relation, serve as gateways among logical systems. Negation therefore plays an important role in selecting logical systems for particular applications. This volume provides a thorough treatment of this concept, based on contributions written by authors from various branches of logic. The resulting 14 research papers address a variety of topics including negation in relevant logics; a defense of dialetheic theory of negation; stable (...)
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  42.  22
    Generalized truth values.: A reply to Dubois.Heinrich Wansing & Nuel Belnap - 2010 - Logic Journal of the IGPL 18 (6):921-935.
  43.  67
    Connectives stranger than tonk.Heinrich Wansing - 2006 - Journal of Philosophical Logic 35 (6):653 - 660.
    Many logical systems are such that the addition of Prior's binary connective tonk to them leads to triviality, see [1, 8]. Since tonk is given by some introduction and elimination rules in natural deduction or sequent rules in Gentzen's sequent calculus, the unwanted effects of adding tonk show that some kind of restriction has to be imposed on the acceptable operational inferences rules, in particular if these rules are regarded as definitions of the operations concerned. In this paper, a number (...)
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  44.  17
    On the Provable Contradictions of the Connexive Logics C and C3.Satoru Niki & Heinrich Wansing - 2023 - Journal of Philosophical Logic 52 (5):1355-1383.
    Despite the tendency to be otherwise, some non-classical logics are known to validate formulas that are invalid in classical logic. A subclass of such systems even possesses pairs of a formula and its negation as theorems, without becoming trivial. How should these provable contradictions be understood? The present paper aims to shed light on aspects of this phenomenon by taking as samples the constructive connexive logic C, which is obtained by a simple modification of a system of constructible falsity, namely (...)
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  45.  22
    A Note On Negation In Categorial Grammar.Heinrich Wansing - 2007 - Logic Journal of the IGPL 15 (3):271-286.
    A version of strong negation is introduced into Categorial Grammar. The resulting syntactic calculi turn out to be systems of connexive logic.
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  46.  53
    Informational interpretation of substructural propositional logics.Heinrich Wansing - 1993 - Journal of Logic, Language and Information 2 (4):285-308.
    This paper deals with various substructural propositional logics, in particular with substructural subsystems of Nelson's constructive propositional logics N– and N. Doen's groupoid semantics is extended to these constructive systems and is provided with an informational interpretation in terms of information pieces and operations on information pieces.
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  47.  77
    Sequent calculi for some trilattice logics.Norihiro Kamide & Heinrich Wansing - 2009 - Review of Symbolic Logic 2 (2):374-395.
    The trilattice SIXTEEN3 introduced in Shramko & Wansing (2005) is a natural generalization of the famous bilattice FOUR2. Some Hilbert-style proof systems for trilattice logics related to SIXTEEN3 have recently been studied (Odintsov, 2009; Shramko & Wansing, 2005). In this paper, three sequent calculi GB, FB, and QB are presented for Odintsovs coordinate valuations associated with valuations in SIXTEEN3. The equivalence between GB, FB, and QB, the cut-elimination theorems for these calculi, and the decidability of B are proved. In addition, (...)
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  48.  24
    Combining linear-time temporal logic with constructiveness and paraconsistency.Norihiro Kamide & Heinrich Wansing - 2010 - Journal of Applied Logic 8 (1):33-61.
  49. From BDI and stit to bdi-stit logic.Caroline Semmling & Heinrich Wansing - 2008 - Logic and Logical Philosophy 17 (1-2):185-207.
    Since it is desirable to be able to talk about rational agents forming attitudes toward their concrete agency, we suggest an introduction of doxastic, volitional, and intentional modalities into the multi-agent logic of deliberatively seeing to it that, dstit logic. These modalities are borrowed from the well-known BDI (belief-desire-intention) logic. We change the semantics of the belief and desire operators from a relational one to a monotonic neighbourhood semantic in order to handle ascriptions of conflicting but not inconsistent beliefs and (...)
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  50.  15
    On Non-transitive “Identity”.Heinrich Wansing & Daniel Skurt - 2019 - In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency. Cham, Switzerland: Springer Verlag. pp. 535-553.
    Graham Priest takes the relation of identity to be non-transitive. In this paper, we are going to discuss several consequences of identity as a non-transitive relation. We will consider the Henkin-style completeness proof for classical first-order logic with a non-transitive “identity” predicate, Leibniz-identity in Priest’s second-order minimal logic of paradox, and the question whether or not identity of individuals should be defined as Leibniz-identity.
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