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43Disentangling FDE -Based Paraconsistent Modal LogicsStudia Logica 105 (6): 1221-1254. 2017.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 absur…Read more
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2"This volume comprises the proceedings of the First All-Berlin Workshop on Nonclassical Logics and Information Processing, held at the Free University of Berlin, November 9-10, 1990. The scope of the ten papers in the volume is broad, covering various different subfields of logic - particularly nonclassical logic - and its applications in artificial intelligence. The papers are grouped according to the four major topics that emerged at the meeting: modal systems, logic programming, nonmonotonic …Read more
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40Proof theory of modal logic (edited book)Kluwer Academic Publishers. 1996.Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.
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62Reprint of: A more general general proof theoryJournal of Applied Logic 25 23-46. 2017.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 pro…Read more
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6Reasoning About Belief RevisionIn Erik J. Olson Sebastian Enqvist (ed.), Belief Revision Meets Philosophy of Science, Springer. pp. 303--328. 2011.
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10Editorial introduction. Special issue on consequence relations and sequent systemsLogic Journal of the IGPL 6 (3): 377-381. 1998.
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5We study a propositional bimodal logic consisting of two S4 modalities £ and [a], together with the interaction axiom scheme a £ϕ → £ aϕ. In the intended semantics, the plain £ is given the McKinsey-Tarski interpretation as the interior operator of a topology, while the labelled [a] is given the standard Kripke semantics using a reflexive and transitive binary relation a. The interaction axiom expresses the property that the Ra relation is lower semi-continuous with respect to the topology. The c…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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34Synchronized Linear-Time Temporal LogicStudia Logica 99 (1-3): 365-388. 2011.A new combined temporal logic called synchronized linear-time temporal logic (SLTL) is introduced as a Gentzen-type sequent calculus. SLTL can represent the n -Cartesian product of the set of natural numbers. The cut-elimination and completeness theorems for SLTL are proved. Moreover, a display sequent calculus δ SLTL is defined.
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27A 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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76Logical Connectives for Constructive Modal LogicSynthese 150 (3): 459-482. 2006.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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46An Axiomatic System and a Tableau Calculus for STIT Imagination LogicJournal of Philosophical Logic 47 (2): 259-279. 2018.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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83Diamonds are a philosopher's best friendsJournal of Philosophical Logic 31 (6): 591-612. 2002.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 derived …Read more
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9Translation of hypersequents into display sequentsLogic Journal of the IGPL 6 (5): 719-734. 1998.
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31Bemerkungen Zur Semantik Nicht-Normaler Möglicher WeltenZeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (6): 551-557. 1989.
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10Strong Cut-Elimination for Constant Domain First-Order S5Logic Journal of the IGPL 3 (5): 797-810. 1995.We consider a labelled tableau presentation of constant domain first-order S5 and prove a strong cut-elimination theorem.
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13Recent Trends in Philosophical Logic (Proceedings of Trends in Logic XI) (edited book)Springer. 2014.This volume presents recent advances in philosophical logic with chapters focusing on non-classical logics, including paraconsistent logics, substructural logics, modal logics of agency and other modal logics. The authors cover themes such as the knowability paradox, tableaux and sequent calculi, natural deduction, definite descriptions, identity, truth, dialetheism and possible worlds semantics. The developments presented here focus on challenging problems in the specification of fundamental ph…Read more
Areas of Specialization
Epistemology |
Logic and Philosophy of Logic |
Areas of Interest
Philosophy of Language |