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38Normality, Non-contamination and Logical Depth in Classical Natural DeductionStudia Logica 108 (2): 291-357. 2020.In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard Gentzen-style natural deduction, (ii) admits of a simple normalization procedure such that normal proofs enjoy the Weak Subformula Property, (iii) provides the means to prove a Non-contamination Property of normal proofs that is not satisfied by normal proofs in the Gentzen tradition and is useful f…Read more
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Dynamics of Practical Reasoning: A Position PaperIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 197-242. 1998.
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16Embedding and Automating Conditional Logics in Classical Higher-Order LogicAnnals of Mathematics and Artificial Intelligence 66 (1-4): 257-271. 2012.
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26Meta-Argumentation Modelling I: Methodology and TechniquesStudia Logica 93 (2-3): 297-355. 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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Investigations in Modal and Tense Logics with Applications to Problems in Philosophy and LinguisticsSynthese 40 (2): 353-373. 1979.
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8Fibred Semantics and the Weaving of Logics Part 1: Modal and Intuitionistic LogicsJournal of Symbolic Logic 61 (3): 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 $\mathbf{L}_i, i \in I$, to form a new system $\mathbf{L}_I$. The methodology `fibres' the semantics $\mathscr{K}_i$ of $\mathbf{L}_i$ into a semantics for $\mathbf{L}_I$, and `weaves' the proof theory of $\mathbf{L}_i$ into a proof system of $\mathbf{L}_I$. There are various ways of doing this, we distinguish by different names such as `fibring', `dov…Read more
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Interpolation and DefinabilityIn D. M. Gabbay & L. L. Maksimova (eds.), ¸ Itegabbay2011, Springer. 2011.
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11Belief 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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32REVIEWS-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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24Computation 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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81Labelled 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