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Heinrich Wansing
Ruhr-Universität Bochum
  1.  86
    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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  2.  59
    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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  3.  64
    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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  4.  18
    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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  5.  11
    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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  6.  11
    Connexive Conditional Logic. Part I.Heinrich Wansing & Matthias Unterhuber - forthcoming - Logic and Logical Philosophy:1.
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  7.  32
    Constructive Negation, Implication, and Co-Implication.Heinrich Wansing - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):341-364.
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  8.  42
    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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  9. 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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  10.  11
    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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  11. Displaying Modal Logic.Heinrich Wansing - 2000 - Studia Logica 66 (3):421-426.
  12.  20
    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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  13.  52
    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 two-valuedness are critically discussed. Another analysis is presented, which favors a notion of a logical system as encompassing possibly more than one consequence relation.
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  14.  8
    Inference as Doxastic Agency. Part I: The Basics of Justification Stit Logic.Grigory K. Olkhovikov & Heinrich Wansing - forthcoming - Studia Logica:1-28.
    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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  15.  33
    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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  16.  15
    Modal Logics with Belnapian Truth Values.Serge P. Odintsov & Heinrich Wansing - 2010 - Journal of Applied Non-Classical Logics 20 (3):279-304.
  17.  52
    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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  18.  2
    A More General General Proof Theory.Heinrich Wansing - 2017 - Journal of Applied Logic 25:23-46.
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  19.  7
    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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  20.  8
    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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  21.  85
    The Slingshot Argument and Sentential Identity.Yaroslav Shramko & Heinrich Wansing - 2009 - Studia Logica 91 (3):429-455.
    The famous “slingshot argument” developed by Church, Gödel, Quine and Davidson is often considered to be a formally strict proof of the Fregean conception that all true sentences, as well as all false ones, have one and the same denotation, namely their corresponding truth value: the true or the false . In this paper we examine the analysis of the slingshot argument by means of a non-Fregean logic undertaken recently by A.Wóitowicz and put to the test her claim that the (...)
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  22.  5
    Combining Linear-Time Temporal Logic with Constructiveness and Paraconsistency.Norihiro Kamide & Heinrich Wansing - 2010 - Journal of Applied Logic 8 (1):33-61.
  23.  32
    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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  24.  60
    Doxastic Decisions, Epistemic Justification, and The Logic of Agency.Heinrich Wansing - 2006 - Philosophical Studies 128 (1):201-227.
    A prominent issue in mainstream epistemology is the controversy about doxastic obligations and doxastic voluntarism. In the present paper it is argued that this discussion can benefit from forging links with formal epistemology, namely the combined modal logic of belief, agency, and obligation. A stit-theory-based semantics for deontic doxastic logic is suggested, and it is claimed that this is helpful and illuminating in dealing with the mentioned intricate and important problems from mainstream epistemology. Moreover, it is argued that this linking (...)
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  25.  41
    The Power of Belnap: Sequent Systems for SIXTEEN ₃. [REVIEW]Heinrich Wansing - 2010 - Journal of Philosophical Logic 39 (4):369 - 393.
    The trilattice SIXTEEN₃ is a natural generalization of the wellknown bilattice FOUR₂. Cut-free, sound and complete sequent calculi for truth entailment and falsity entailment in SIXTEEN₃, are presented.
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  26.  75
    A Non-Inferentialist, Anti-Realistic Conception of Logical Truth and Falsity.Heinrich Wansing - 2012 - Topoi 31 (1):93-100.
    Anti-realistic conceptions of truth and falsity are usually epistemic or inferentialist. Truth is regarded as knowability, or provability, or warranted assertability, and the falsity of a statement or formula is identified with the truth of its negation. In this paper, a non-inferentialist but nevertheless anti-realistic conception of logical truth and falsity is developed. According to this conception, a formula (or a declarative sentence) A is logically true if and only if no matter what is told about what is told about (...)
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  27. What Is Negation?Dov M. Gabbay & Heinrich Wansing - 2001 - Studia Logica 69 (3):435-439.
  28.  19
    Displaying the Modal Logic of Consistency.Heinrich Wansing - 1999 - Journal of Symbolic Logic 64 (4):1573-1590.
    It is shown that the constructive four-valued logic N4 can be faithfully embedded into the modal logic S4. This embedding is used to obtain complete, cut-free display sequent calculi for N4 and C4, the modal logic of consistency over N4. C4 is a natural monotonic base system for semantics-based non-monotonic reasoning.
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  29.  60
    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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  30.  2
    Advances in Modal Logic.Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev - 2002 - Bulletin of Symbolic Logic 8 (1):95-97.
  31.  7
    Generalized Truth Values.: A Reply to Dubois.Heinrich Wansing & Nuel Belnap - 2010 - Logic Journal of the IGPL 18 (6):921-935.
  32.  57
    Logical Connectives for Constructive Modal Logic.Heinrich Wansing - 2006 - Synthese 150 (3):459-482.
    Model-theoretic proofs of functional completenes along the lines of [McCullough 1971, Journal of Symbolic Logic 36, 15–20] are given for various constructive modal propositional logics with strong negation.
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  33.  38
    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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  34.  13
    Connexive Logic.Heinrich Wansing - 2008 - Stanford Encyclopedia of Philosophy.
  35.  21
    Reprint Of: A More General General Proof Theory.Heinrich Wansing - 2017 - Journal of Applied Logic 25:23-46.
    In this paper it is suggested to generalize our understanding of general (structural) proof theory and to consider it as a general theory of two kinds of derivations, namely proofs and dual proofs. The proposal is substantiated by (i) considerations on assertion, denial, and bi-lateralism, (ii) remarks on compositionality in proof-theoretic semantics, and (iii) comments on falsification and co-implication. The main formal result of the paper is a normal form theorem for the natural deduction proof system N2Int of the bi-intuitionistic (...)
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  36.  32
    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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  37.  5
    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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  38. Normative Verantwortung für Handlungen Anderer. Eine Untersuchung im Rahmen der stit-Theorie.Sarah Ganter & Heinrich Wansing - 2005 - Facta Philosophica 7 (2):167-187.
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  39.  32
    Nested Deontic Modalities: Another View of Parking on Highways. [REVIEW]Heinrich Wansing - 1998 - Erkenntnis 49 (2):185-199.
    A suggestion is made for representing iterated deontic modalities in stit theory, the “seeing-to-it-that” theory of agency. The formalization is such that normative sentences are represented as agentive sentences and therefore have history dependent truth conditions. In contrast to investigations in alethic modal logic, in the construction of systems of deontic logic little attention has been paid to the iteration... of the deontic modalities.
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  40.  1
    Action-Theoreticaspects of Theory Choice.Heinrich Wansing - 2004 - In S. Rahman J. Symons (ed.), Logic, Epistemology, and the Unity of Science. Kluwer Academic Publisher. pp. 419--435.
  41.  13
    Entailment Relations and/as Truth Values.Yaroslav Shramko & Heinrich Wansing - 2007 - Bulletin of the Section of Logic 36 (3/4):131-143.
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  42.  4
    Seeing to It That an Agent Forms a Belief.Heinrich Wansing - 2002 - Logic and Logical Philosophy 10:185.
  43.  17
    Semantics-Based Nonmonotonic Inference.Heinrich Wansing - 1995 - Notre Dame Journal of Formal Logic 36 (1):44-54.
    In this paper we discuss Gabbay's idea of basing nonmonotonic deduction on semantic consequence in intuitionistic logic extended by a consistency operator and Turner's suggestion of replacing the intuitionistic base system by Kleene's three-valued logic. It is shown that a certain counterintuitive feature of these approaches can be avoided by using Nelson's constructive logic N instead of intuitionistic logic or Kleene's system. Moreover, in N a more general notion of consistency can be defined and nonmonotonic deduction can thus be based (...)
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  44.  15
    Editorial Introduction. Truth Values: Part II. [REVIEW]Yaroslav Shramko & Heinrich Wansing - 2009 - Studia Logica 92 (2):143-146.
  45.  40
    Erratum to Suszko's Thesis, Inferential Many-Valuedness, and the Notion of a Logical System Studia Logica , 88:405–429, 2008. [REVIEW]Heinrich Wansing & Yaroslav Shramko - 2008 - Studia Logica 89 (1):147-147.
  46.  8
    Symmetric and Dual Paraconsistent Logics.Norihiro Kamide & Heinrich Wansing - 2010 - Logic and Logical Philosophy 19 (1-2):7-30.
    Two new first-order paraconsistent logics with De Morgan-type negations and co-implication, called symmetric paraconsistent logic (SPL) and dual paraconsistent logic (DPL), are introduced as Gentzen-type sequent calculi. The logic SPL is symmetric in the sense that the rule of contraposition is admissible in cut-free SPL. By using this symmetry property, a simpler cut-free sequent calculus for SPL is obtained. The logic DPL is not symmetric, but it has the duality principle. Simple semantics for SPL and DPL are introduced, and the (...)
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  47.  31
    Predicate Logics on Display.Heinrich Wansing - 1999 - Studia Logica 62 (1):49-75.
    The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem''s modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap''s display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or its converse to (...)
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  48.  32
    Introduction to the Special Issue “Doxastic Agency and Epistemic Responsibility”.Andrea Kruse & Heinrich Wansing - 2017 - Synthese 194 (8):2667-2671.
  49.  19
    A Reduction of Doxastic Logic to Action Logic.Heinrich Wansing - 2000 - Erkenntnis 53 (1-2):267-283.
  50.  17
    Bemerkungen Zur Semantik Nicht-Normaler Möglicher Welten.Heinrich Wansing - 1989 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (6):551-557.
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