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45Disentangling 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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66Reprint 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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78Contradiction and contrariety. Priest on negationPoznan Studies in the Philosophy of the Sciences and the Humanities 91 (1): 81-93. 2006.Although it is not younger than other areas of non-classical logic, paraconsistent logic has received full recognition only in recent years, largely due to the work of, among others, Newton da Costa, Graham Priest, Diderik Batens, and Jerzy Perzanowski. A logical system Λ is paraconsistent if there is a set of Λ-formulas Δ ∪ {A} such that in Λ one may derive from Δ both A and its negation, and the deductive closure of Δ with respect to Λ is different from the set of all formulas. If from Δ one m…Read more
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Strong Cut-elimination In Display LogicReports on Mathematical Logic 117-131. 1995.It is shown that every displayable propositional logic enjoys strong cut-elimination. This result strengthens Belnap's general cut-elimination theorem for Display Logic.
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42On the methodology of possible worlds semantics. I. Correspondence theoryNotre Dame Journal of Formal Logic 29 (4): 482-496. 1988.
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23A 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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49Displaying 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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52Modal logics with Belnapian truth valuesJournal of Applied Non-Classical Logics 20 (3): 279-304. 2010.Various four- and three-valued modal propositional logics are studied. The basic systems are modal extensions BK and BS4 of Belnap and Dunn's four-valued logic of firstdegree entailment. Three-valued extensions of BK and BS4 are considered as well. These logics are introduced semantically by means of relational models with two distinct evaluation relations, one for verification and the other for falsification. Axiom systems are defined and shown to be sound and complete with respect to the relat…Read more
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68Connectives stranger than tonkJournal of Philosophical Logic 35 (6). 2006.Many logical systems are such that the addition of Prior's binary connective tonk to them leads to triviality, see [1, 8]. Since tonk is given by some introduction and elimination rules in natural deduction or sequent rules in Gentzen's sequent calculus, the unwanted effects of adding tonk show that some kind of restriction has to be imposed on the acceptable operational inferences rules, in particular if these rules are regarded as definitions of the operations concerned. In this paper, a numbe…Read more
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91The Idea of a Proof-Theoretic Semantics and the Meaning of the Logical OperationsStudia Logica 64 (1): 3-20. 2000.This is a purely conceptual paper. It aims at presenting and putting into perspective the idea of a proof-theoretic semantics of the logical operations. The first section briefly surveys various semantic paradigms, and Section 2 focuses on one particular paradigm, namely the proof-theoretic semantics of the logical operations.
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32Symmetric 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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127Remarks on the logic of imagination. A step towards understanding doxastic control through imaginationSynthese 194 (8): 2843-2861. 2017.Imagination has recently attracted considerable attention from epistemologists and is recognized as a source of belief and even knowledge. One remarkable feature of imagination is that it is often and typically agentive: agents decide to imagine. In cases in which imagination results in a belief, the agentiveness of imagination may be taken to give rise to indirect doxastic control and epistemic responsibility. This observation calls for a proper understanding of agentive imagination. In particu…Read more
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20Formal Philosophy - Edited by Vincent F. Hendricks and John SymonsPhilosophical Books 48 (2): 172-173. 2007.
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97A general possible worlds framework for reasoning about knowledge and beliefStudia Logica 49 (4). 1990.In this paper non-normal worlds semantics is presented as a basic, general, and unifying approach to epistemic logic. The semantical framework of non-normal worlds is compared to the model theories of several logics for knowledge and belief that were recently developed in Artificial Intelligence (AI). It is shown that every model for implicit and explicit belief (Levesque), for awareness, general awareness, and local reasoning (Fagin and Halpern), and for awareness and principles (van der Hoek a…Read more
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70External CurriesJournal of Philosophical Logic 44 (4): 453-471. 2015.Curry’s paradox is well known. The original version employed a conditional connective, and is not forthcoming if the conditional does not satisfy contraction. A newer version uses a validity predicate, instead of a conditional, and is not forthcoming if validity does not satisfy structural contraction. But there is a variation of the paradox which uses “external validity”. And since external validity contracts, one might expect the appropriate version of the Curry paradox to be inescapable. In t…Read more
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425From BDI and stit to bdi-stit logicLogic and Logical Philosophy 17 (1-2): 185-207. 2008.Since it is desirable to be able to talk about rational agents forming attitudes toward their concrete agency, we suggest an introduction of doxastic, volitional, and intentional modalities into the multi-agent logic of deliberatively seeing to it that, dstit logic. These modalities are borrowed from the well-known BDI (belief-desire-intention) logic. We change the semantics of the belief and desire operators from a relational one to a monotonic neighbourhood semantic in order to handle ascripti…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
Areas of Specialization
Epistemology |
Logic and Philosophy of Logic |
Areas of Interest
Philosophy of Language |