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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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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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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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89The 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
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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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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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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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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.
Areas of Specialization
Epistemology |
Logic and Philosophy of Logic |
Areas of Interest
Philosophy of Language |