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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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4"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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65Reprint 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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23Tarskian 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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5Action-Theoreticaspects of Theory ChoiceIn S. Rahman J. Symons (ed.), Logic, Epistemology, and the Unity of Science, Kluwer Academic Publisher. pp. 419--435. 2004.
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40Predicate logics on displayStudia Logica 62 (1): 49-75. 1999.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 the…Read more
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Thomas Andreas Meyer, Willem Adrian Labuschagne, and Johannes heidema/refined espistemic entrenchment 237-259Journal of Logic, Language, and Information 9 (2): 139. 1992.
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53Informational interpretation of substructural propositional logicsJournal of Logic, Language and Information 2 (4): 285-308. 1993.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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38The Logic of Generalized Truth Values and the Logic of BilatticesStudia Logica 103 (1): 91-112. 2015.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 bil…Read more
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1Displaying the Modal Logic of ConsistencyJournal of Symbolic Logic 64 (4): 1573-1590. 1999.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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77Sequent calculi for some trilattice logicsReview of Symbolic Logic 2 (2): 374-395. 2009.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…Read more
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42Correction to ‘Displaying the modal logic of consistency’Journal of Symbolic Logic 68 (2): 712-712. 2003.
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11Review: Review of Modal Logic P. Blackburn, M. de Rijke, Y. Venema: Review of Modal Logic (review)Logic Journal of the IGPL 10 (4): 457-458. 2002.
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49Semantics-based Nonmonotonic InferenceNotre Dame Journal of Formal Logic 36 (1): 44-54. 1995.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 …Read more
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20Bemerkungen Zur Semantik Nicht‐Normaler Möglicher WeltenMathematical Logic Quarterly 35 (6): 551-557. 1989.
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31Hypersequent 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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104A Non-Inferentialist, Anti-Realistic Conception of Logical Truth and FalsityTopoi 31 (1): 93-100. 2012.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 to…Read more
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48Nested deontic modalities: Another view of parking on highways (review)Erkenntnis 49 (2): 185-199. 1998.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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6Reasoning About Belief RevisionIn Erik J. Olson Sebastian Enqvist (ed.), Belief Revision Meets Philosophy of Science, Springer. pp. 303--328. 2011.
Areas of Specialization
Epistemology |
Logic and Philosophy of Logic |
Areas of Interest
Philosophy of Language |