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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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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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84Diamonds 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
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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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50Functional completeness for subsystems of intuitionistic propositional logicJournal of Philosophical Logic 22 (3). 1993.
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9Dag Prawitz on Proofs and Meaning (edited book)Springer. 2015.This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD t…Read more
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15Advances in Modal Logic, Volume 2: Papers From the Second Aiml Conference, Held at the University of Uppsala, Sweden, October 1998 (edited book)Center for the Study of Language and Inf. 2001.Modal Logic, originally conceived as the logic of necessity and possibility, has developed into a powerful mathematical and computational discipline. It is the main source of formal languages aimed at analyzing complex notions such as common knowledge and formal provability. Modal and modal-like languages also provide us with families of restricted description languages for relational and topological structures; they are being used in many disciplines, ranging from artificial intelligence, compu…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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89Constructive negation, implication, and co-implicationJournal of Applied Non-Classical Logics 18 (2-3): 341-364. 2008.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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24Combining linear-time temporal logic with constructiveness and paraconsistencyJournal of Applied Logic 8 (1): 33-61. 2010.
Areas of Specialization
Epistemology |
Logic and Philosophy of Logic |
Areas of Interest
Philosophy of Language |