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31Symmetric and dual paraconsistent logicsLogic and Logical Philosophy 19 (1-2): 7-30. 2010.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…Read more
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30Hypersequent and Display Calculi – a Unified PerspectiveStudia Logica 102 (6): 1245-1294. 2014.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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30On Definability of Connectives and Modal Logics over FDELogic and Logical Philosophy 1. forthcoming.
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29PrefaceLogic 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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28A rule-extension of the non-associative Lambek calculusStudia Logica 71 (3): 443-451. 2002.An extension L + of the non-associative Lambek calculus Lis defined. In L + the restriction to formula-conclusion sequents is given up, and additional left introduction rules for the directional implications are introduced. The system L + is sound and complete with respect to a modification of the ternary frame semantics for L.
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27New Essays on Belnap-Dunn Logic (edited book)Springer Verlag. 2019.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…Read more
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26Constructive 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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25A fugue on the themes of awareness logic and correspondenceJournal of Applied Non-Classical Logics 6 (2): 127-136. 1996.No abstract
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24Combining linear-time temporal logic with constructiveness and paraconsistencyJournal of Applied Logic 8 (1): 33-61. 2010.
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24Connexive Modal LogicIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 367-383. 1998.
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22A Note On Negation In Categorial GrammarLogic Journal of the IGPL 15 (3): 271-286. 2007.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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22Tarskian Structured Consequence Relations and Functional CompletenessMathematical Logic Quarterly 41 (1): 73-92. 1995.In this paper functional completeness results are obtained for certain positive and constructive propositional logics associated with a Tarski-type structured consequence relation as defined by Gabbay
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22Connexive Modal LogicIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 367-383. 1998.
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21Nino B. Cocchiarella and Max A. Freund. Modal logic. An introduction to its syntax and semantics. Oxford University Press, Oxford, 2008, xi + 268 pp (review)Bulletin of Symbolic Logic 16 (2): 275-276. 2010.
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20Bemerkungen Zur Semantik Nicht‐Normaler Möglicher WeltenMathematical Logic Quarterly 35 (6): 551-557. 1989.
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20Truth and Falsehood: An Inquiry Into Generalized Logical ValuesSpringer. 2011.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 multilatt…Read more
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20Inconsistency-tolerant description logic. Part II: A tableau algorithm for CALC CJournal of Applied Logic 6 (3): 343-360. 2008.
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20Formal Philosophy - Edited by Vincent F. Hendricks and John SymonsPhilosophical Books 48 (2): 172-173. 2007.
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18On 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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18Completeness and cut-elimination theorems for trilattice logicsAnnals of Pure and Applied Logic 162 (10): 816-835. 2011.A sequent calculus for Odintsov’s Hilbert-style axiomatization of a logic related to the trilattice SIXTEEN3 of generalized truth values is introduced. The completeness theorem w.r.t. a simple semantics for is proved using Maehara’s decomposition method that simultaneously derives the cut-elimination theorem for . A first-order extension of and its semantics are also introduced. The completeness and cut-elimination theorems for are proved using Schütte’s method.
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18Simplified Tableaux for STIT Imagination LogicJournal of Philosophical Logic 48 (6): 981-1001. 2019.We show how to correct the analytic tableaux system from the paper Olkhovikov and Wansing, 259–279, 2018).
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17Truth Values. Part IStudia 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 f…Read more
Areas of Specialization
Epistemology |
Logic and Philosophy of Logic |
Areas of Interest
Philosophy of Language |