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5An Invitation to New Essays on Belnap-Dunn LogicIn Hitoshi Omori & Heinrich Wansing (eds.), New Essays on Belnap-Dunn Logic, Springer Verlag. pp. 1-9. 2019.In this introductory note, we place the new essays on Belnap-Dunn logic, FDE, of the present volume against the background of the development of FDE. This note is an invitation to study the volume. It presents a chronological perspective on Belnap-Dunn logic and a slightly idiosyncratic list of further research topics.
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4Interview with Prof. Nuel D. BelnapIn Hitoshi Omori & Heinrich Wansing (eds.), New Essays on Belnap-Dunn Logic, Springer Verlag. pp. 99-111. 2019.The interview between Nuel D. Belnap and Heinrich Wansing took place in Pittsburgh on November the 5th, 2015. The text below is a slightly edited version of the transcript based on the recording (We are grateful to Mrs Claudia Smart for the careful transcription and to Nuel Belnap for his approval of it.).
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6On the Methodology of Paraconsistent LogicIn Peter Verdée & Holger Andreas (eds.), Logical Studies of Paraconsistent Reasoning in Science and Mathematics, Springer Verlag. pp. 175-204. 2016.The present note contains a critical discussion of the methodology of paraconsistent logic in general and “the central optimisation problem of paraconsistent logics” in particular. It is argued that there exist several reasons not to consider classical logic as the reference logic for developing systems of paraconsistent logic, and it is suggested to weaken a certain maximality condition that may be seen as essential for “optimisation”, which is a methodology in the tradition of Newton da Costa.…Read more
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18Bi-Connexive Logic, Bilateralism, and Negation InconsistencyReview of Symbolic Logic 1-41. forthcoming.In this paper we study logical bilateralism understood as a theory of two primitive derivability relations, namely provability and refutability, in a language devoid of a primitive strong negation and without a falsum constant, $\bot $, and a verum constant, $\top $. There is thus no negation that toggles between provability and refutability, and there are no primitive constants that are used to define an “implies falsity” negation and a “co-implies truth” co-negation. This reduction of expressi…Read more
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28Quantifiers in connexive logic (in general and in particular)Logic Journal of the IGPL. forthcoming.Connexive logic has room for two pairs of universal and particular quantifiers: one pair, |$\forall $| and |$\exists $|, are standard quantifiers; the other pair, |$\mathbb{A}$| and |$\mathbb{E}$|, are unorthodox, but we argue, are well-motivated in the context of connexive logic. Both non-standard quantifiers have been introduced previously, but in the context of connexive logic they have a natural semantic and proof-theoretic place, and plausible natural language readings. The results are lo…Read more
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24Substructural Negations as Normal Modal OperatorsIn Yale Weiss & Romina Birman (eds.), Saul Kripke on Modal Logic. pp. 365-388. 2024.A theory of substructural negations as impossibility and as unnecessity based on bi-intuitionistic logic, also known as Heyting-Brouwer logic, has been developed by Takuro Onishi. He notes two problems for that theory and offers the identification of the two negations as a solution to both problems. The first problem is the lack of a structural rule corresponding with double negation elimination for negation as impossibility, DNE, and the second problem is a lack of correspondence between certai…Read more
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19Connexive ExclusionErkenntnis 1-32. forthcoming.We present a logic which deals with connexive exclusion. Exclusion (also called “co-implication”) is considered to be a propositional connective dual to the connective of implication. Similarly to implication, exclusion turns out to be non-connexive in both classical and intuitionistic logics, in the sense that it does not satisfy certain principles that express such connexivity. We formulate these principles for connexive exclusion, which are in some sense dual to the well-known Aristotle’s and…Read more
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40Entailment relations and/as truth valuesBulletin of the Section of Logic 36 (3/4): 131-143. 2007.
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27A Note on Synonymy in Proof-Theoretic SemanticsIn Thomas Piecha & Kai F. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics, Springer Nature Switzerland. pp. 339-362. 2024.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 questi…Read more
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64Constructive Logic is Connexive and ContradictoryLogic and Logical Philosophy 1-27. forthcoming.It is widely accepted that there is a clear sense in which the first-order paraconsistent constructive logic with strong negation of Almukdad and Nelson, QN4, is more constructive than intuitionistic first-order logic, QInt. While QInt and QN4 both possess the disjunction property and the existence property as characteristics of constructiveness (or constructivity), QInt lacks certain features of constructiveness enjoyed by QN4, namely the constructible falsity property and the dual of the exist…Read more
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45Connexive Logic, Connexivity, and Connexivism: Remarks on TerminologyStudia Logica 112 (1): 1-35. 2023.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 will make clear…Read more
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36The 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 multilatt…Read more
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64Logical MultilateralismJournal of Philosophical Logic 52 (6): 1603-1636. 2023.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 seque…Read more
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49On the Provable Contradictions of the Connexive Logics C and C3Journal of Philosophical Logic 52 (5): 1355-1383. 2023.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…Read more
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41On Synonymy in Proof-Theoretic Semantics: The Case of \(\mathtt{2Int}\)Bulletin of the Section of Logic 52 (2): 187-237. 2023.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 ar…Read more
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43NegationIn Lou Goble (ed.), The Blackwell Guide to Philosophical Logic, Wiley-blackwell. 2001.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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24Proofs and Expressiveness in Alethic Modal LogicIn Dale Jacquette (ed.), A Companion to Philosophical Logic, Wiley-blackwell. 2002.This chapter contains sections titled: Introduction Model Theory Proof Theory Modal Predicate Logic.
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8740 years of FDE: An Introductory OverviewStudia Logica 105 (6): 1021-1049. 2017.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 some…Read more
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79On contra-classical variants of Nelson logic n4 and its classical extensionReview of Symbolic Logic 11 (4): 805-820. 2018.
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57Kripke Completeness of Bi-intuitionistic Multilattice Logic and its Connexive VariantStudia Logica 105 (6): 1193-1219. 2017.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-i…Read more
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126Suszko’s Thesis, Inferential Many-valuedness, and the Notion of a Logical SystemStudia Logica 88 (3): 405-429. 2008.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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77Connexive Conditional Logic. Part ILogic and Logical Philosophy 28 (3): 567-610. 2019.In this paper, first some propositional conditional logics based on Belnap and Dunn’s useful four-valued logic of first-degree entailment are introduced semantically, which are then turned into systems of weakly and unrestrictedly connexive conditional logic. The general frame semantics for these logics makes use of a set of allowable (or admissible) extension/antiextension pairs. Next, sound and complete tableau calculi for these logics are presented. Moreover, an expansion of the basic conditi…Read more
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63PrefaceLogic and Logical Philosophy 3 (n/a): 45-46. 1995.Science today is an international business, of course, and there has hardly ever been a partition wall between the logical work in Poland and Germany. However, apart from long lasting personal scientific contacts there are good reasons to further intensify the relations between the German and the Polish Community of Logic and Logical Philosophy. So it was only natural to think about bringing them together at a scientific event in a friendly environment. This idea was carried out as a common init…Read more
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208The Slingshot Argument and Sentential IdentityStudia Logica 91 (3): 429-455. 2009.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 slingshot argument is in …Read more
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164Some Useful 16-Valued Logics: How a Computer Network Should ThinkJournal of Philosophical Logic 34 (2): 121-153. 2005.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 information ordering together with a truth o…Read more
Areas of Specialization
Epistemology |
Logic and Philosophy of Logic |
Areas of Interest
Philosophy of Language |