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Interpolation and DefinabilityIn D. M. Gabbay & L. L. Maksimova (eds.), ¸ Itegabbay2011, Springer. 2011.
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10Belief Contraction, Anti-formulae and Resource Overdraft: Part I Deletion in Resource bounded LogicsLogic Journal of the IGPL 10 (5): 501-549. 2002.There are several areas in applied logic where deletion from databases is involved in one way or another:Belief contraction Triggers of the form ‘If condition then remove A’, which are extensively used in database management systemsResource considerations as in relevance and linear logics, where addition or removal of resource can affect provabilityFree logic and the like, where existence and non-existence of individuals affects quantification.All of these areas have certain logical difficulties…Read more
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29Theory of Semi-Instantiation in Abstract ArgumentationLogica Universalis 10 (4): 431-516. 2016.We study instantiated abstract argumentation frames of the form, where is an abstract argumentation frame and where the arguments x of S are instantiated by I as well formed formulas of a well known logic, for example as Boolean formulas or as predicate logic formulas or as modal logic formulas. We use the method of conceptual analysis to derive the properties of our proposed system. We seek to define the notion of complete extensions for such systems and provide algorithms for finding such exte…Read more
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10Interpolation and Definability: Modal and Intuitionistic LogicsOxford University Press UK. 2005.This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language. Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dumm…Read more
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Extending the Curry {Howard {Tait interpretation to linear, relevant and other logicsJournal of Symbolic Logic 56 1129-40. 1992.
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31REVIEWS-Many-dimensional modal logics: Theory and applicationsBulletin of Symbolic Logic 11 (1): 77-78. 2005.
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14Meta-Argumentation Modelling I: Methodology and TechniquesStudia Logica 93 (2-3): 297-354. 2009.In this paper, we introduce the methodology and techniques of meta-argumentation to model argumentation. The methodology of meta-argumentation instantiates Dung’s abstract argumentation theory with an extended argumentation theory, and is thus based on a combination of the methodology of instantiating abstract arguments, and the methodology of extending Dung’s basic argumentation frameworks with other relations among abstract arguments. The technique of meta-argumentation applies Dung’s theory o…Read more
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21Computation with run time skolemisation (N-Prolog part 3)Journal of Applied Non-Classical Logics 3 (1): 93-128. 1993.No abstract
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79Labelled resolution for classical and non-classical logicsStudia Logica 59 (2): 179-216. 1997.Resolution is an effective deduction procedure for classical logic. There is no similar "resolution" system for non-classical logics (though there are various automated deduction systems). The paper presents resolution systems for intuistionistic predicate logic as well as for modal and temporal logics within the framework of labelled deductive systems. Whereas in classical predicate logic resolution is applied to literals, in our system resolution is applied to L(abelled) R(epresentation) S(tru…Read more
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13REVIEWS-Handbook of philosophical logic, vol. 10Bulletin of Symbolic Logic 13 (2): 248-250. 2007.
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22A Sequence of Decidable Finitely Axiomatizable Intermediate Logics with the Disjunction PropertyJournal of Symbolic Logic 39 (1). 1974.
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39Equational approach to argumentation networksArgument and Computation 3 (2-3). 2012.This paper provides equational semantics for Dung's argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the ?extensions? of the network. This approach is very general and includes the Caminada labelling as a special case, as well as many other so-called network extensions, support systems, higher level attacks, Boolean networks, dependence on time, and much more. The equational appr…Read more
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66Naming worlds in modal and temporal logicJournal of Logic, Language and Information 11 (1): 29-65. 2002.In this paper we suggest adding to predicate modal and temporal logic a locality predicate W which gives names to worlds (or time points). We also study an equal time predicate D(x, y)which states that two time points are at the same distance from the root. We provide the systems studied with complete axiomatizations and illustrate the expressive power gained for modal logic by simulating other logics. The completeness proofs rely on the fairly intuitive notion of a configuration in order to use…Read more
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44Undecidability of modal and intermediate first-order logics with two individual variablesJournal of Symbolic Logic 58 (3): 800-823. 1993.
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127A theory of hypermodal logics: Mode shifting in modal logic (review)Journal of Philosophical Logic 31 (3): 211-243. 2002.A hypermodality is a connective □ whose meaning depends on where in the formula it occurs. The paper motivates the notion and shows that hypermodal logics are much more expressive than traditional modal logics. In fact we show that logics with very simple K hypermodalities are not complete for any neighbourhood frames
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47Fibred semantics and the weaving of logics part 1: Modal and intuitionistic logicsJournal of Symbolic Logic 61 (4): 1057-1120. 1996.This is Part 1 of a paper on fibred semantics and combination of logics. It aims to present a methodology for combining arbitrary logical systems L i , i ∈ I, to form a new system L I . The methodology `fibres' the semantics K i of L i into a semantics for L I , and `weaves' the proof theory (axiomatics) of L i into a proof system of L I . There are various ways of doing this, we distinguish by different names such as `fibring', `dovetailing' etc, yielding different systems, denoted by L F I , L…Read more
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107Neural-Symbolic Cognitive ReasoningSpringer. 2009.Humans are often extraordinary at performing practical reasoning. There are cases where the human computer, slow as it is, is faster than any artificial intelligence system. Are we faster because of the way we perceive knowledge as opposed to the way we represent it? The authors address this question by presenting neural network models that integrate the two most fundamental phenomena of cognition: our ability to learn from experience, and our ability to reason from what has been learned. This b…Read more
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25Compiled Labelled Deductive Systems: A Uniform Presentation of Non-classical LogicsInstitute of Physics/Research Studies Press. 2004.K. Broda, Dov M. Gabbay, Alessandra Russo and LuÍs C. Lamb argue that though the many families of logic may seem to differ in their logical nature, it is possible to provide them with a unifying logical framework whenever their semantics is axiomatizable in first-order logic. They provide such a framework based on the labeled deductive system methodology, and demonstrate how it works in such families as normal modal logics, conditional logics of normality, the modal logic of elsewhere, the multi…Read more
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18Łukasiewicz Logic: From Proof Systems To Logic ProgrammingLogic Journal of the IGPL 13 (5): 561-585. 2005.We present logic programming style “goal-directed” proof methods for Łukasiewicz logic Ł that both have a logical interpretation, and provide a suitable basis for implementation. We introduce a basic version, similar to goal-directed calculi for other logics, and make refinements to improve efficiency and obtain termination. We then provide an algorithm for fuzzy logic programming in Rational Pavelka logic RPL, an extension of Ł with rational constants
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99Independence — Revision and DefaultsStudia Logica 92 (3): 381-394. 2009.We investigate different aspects of independence here, in the context of theory revision, generalizing slightly work by Chopra, Parikh, and Rodrigues, and in the context of preferential reasoning.
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25The Functional Interpretation of the Existential QuantifierLogic Journal of the IGPL 3 (2-3): 243-290. 1995.We are concerned with showing how ‘labelled’ Natural Deduction presentation systems based on an extension of the so-called Curry-Howard functional interpretation can help us understand and generalise most of the deduction calculi designed to deal with the logical notion of existential quantification. We present the labelling mechanism for ‘’ using what we call ‘ɛ-terms’, which have the form of ‘a’) in a dual form to the ‘Ax.f’ terms of in the sense that the ‘witness’ is chosen at the time of ass…Read more