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191Proving unprovability in some normal modal logicsBulletin of the Section of Logic 20 (1): 23-29. 1991.This note considers deductive systems for the operator a of unprovability in some particular propositional normal modal logics. We give thus complete syntactic characterization of these logics in the sense of Lukasiewicz: for every formula either ` or a (but not both) is derivable. In particular, purely syntactic decision procedure is provided for the logics under considerations.
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181Modal Logic and Universal Algebra I: Modal Axiomatizations of StructuresIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 265-292. 1998.We study the general problem of axiomatizing structures in the framework of modal logic and present a uniform method for complete axiomatization of the modal logics determined by a large family of classes of structures of any signature.
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127Comparing semantics of logics for multi-agent systemsSynthese 139 (2). 2004.We draw parallels between several closely related logics that combine — in different proportions — elements of game theory, computation tree logics, and epistemic logics to reason about agents and their abilities. These are: the coalition game logics CL and ECL introduced by Pauly 2000, the alternating-time temporal logic ATL developed by Alur, Henzinger and Kupferman between 1997 and 2002, and the alternating-time temporal epistemic logic ATEL by van der Hoek and Wooldridge (2002). In particula…Read more
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94Approximating trees as coloured linear orders and complete axiomatisations of some classes of treesJournal of Symbolic Logic 86 (3): 1035-1065. 2021.We study the first-order theories of some natural and important classes of coloured trees, including the four classes of trees whose paths have the order type respectively of the natural numbers, the integers, the rationals, and the reals. We develop a technique for approximating a tree as a suitably coloured linear order. We then present the first-order theories of certain classes of coloured linear orders and use them, along with the approximating technique, to establish complete axiomatisatio…Read more
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71An extended branching-time ockhamist temporal logicJournal of Logic, Language and Information 8 (2): 143-166. 1999.For branching-time temporal logic based on an Ockhamist semantics, we explore a temporal language extended with two additional syntactic tools. For reference to the set of all possible futures at a moment of time we use syntactically designated restricted variables called fan-names. For reference to all possible futures alternative to the actual one we use a modification of a difference modality, localized to the set of all possible futures at the actual moment of time.We construct an axiomatic …Read more
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51Patrick Blackburn, Maarten de Rijke and Yde Venema, Modal Logic, Cambridge Tracts in Theoretical Computer Science vol. 53 (review)Studia Logica 76 (1): 135-142. 2004.Book review
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44Logic in computer science: Modelling and reasoning about systems (review)Journal of Logic, Language and Information 16 (1): 117-120. 2006.Book review
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41Reasoning about knowledge, Ronald Fagin, Joseph Y. Halpern, Yoram Moses, and Moshe Y. Vardi (review)Journal of Logic, Language and Information 8 (4): 469-473. 1999.
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41Logics for propositional determinacy and independenceReview of Symbolic Logic 11 (3): 470-506. 2018.This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic D and Propositional Independence Logic I are recently developed logical systems, based on team semantics, that provide a framework for such reasoning tasks. We introduce two new logics L_D and L_I, based on Kripke semantics, and propose them as alternatives for D and I, respectively. We analyse the relative expressive powers of these four logics and discuss the way these systems…Read more
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31Modal logic, Alexander Chagrov and Michael Zakharyaschev (review)Journal of Logic, Language and Information 8 (2): 255-258. 1999.Book review
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22Hybrid Deduction–Refutation SystemsAxioms 8 (4). 2019.Hybrid deduction–refutation systems are deductive systems intended to derive both valid and non-valid, i.e., semantically refutable, formulae of a given logical system, by employing together separate derivability operators for each of these and combining ‘hybrid derivation rules’ that involve both deduction and refutation. The goal of this paper is to develop a basic theory and ‘meta-proof’ theory of hybrid deduction–refutation systems. I then illustrate the concept on a hybrid derivation system…Read more
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20Foreword to Special issue on Logics for Multi-agent SystemsJournal of Applied Non-Classical Logics 21 (1): 7-8. 2011.Foreword to Special issue on Logics for Multi-agent Systems
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20ForewordJournal of Applied Non-Classical Logics 14 (1-2): 7-8. 2004.Foreword to the Special issue on Interval Temporal Logics and Duration Calculi
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16Knowledge-based strategies for multi-agent teams playing against NatureArtificial Intelligence 309 (C): 103728. 2022.
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14Patrick Blackburn, Maarten de Rijke and Yde Venema, Cambridge Tracts in Theoretical Computer Science Vol. 53 (review)Studia Logica 76 (1): 135-142. 2004.Book review
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14Advances in Modal Logic 8 (edited book)College Publications. 2010.Proc. of the 8th International Conference on Advances in Modal Logic, (AiML'2010).
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11Algorithmic Correspondence for Relevance Logics I. The Algorithm PEARL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {PEARL}$$\end{document} (review)In Ivo Düntsch & Edwin Mares (eds.), Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs, Springer Verlag. pp. 163-211. 2021.We apply and extend the theory and methods of algorithmic correspondence theory for modal logics, developed over the past 20 years, to the language LR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}_R$$\end{document} of relevance logics with respect to their standard Routley–Meyer relational semantics. We…Read more
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9Elementary Canonical Formulae: A Survey on Syntactic, Algorithmic, and Modeltheoretic AspectsIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 17-51. 1998.In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called \emph{elementary}. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called \emph{canonical}. This is a survey of a recent and ongoing study of the class of elementary …Read more
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8A Logic for Conditional Local Strategic ReasoningJournal of Logic, Language and Information 31 (2): 167-188. 2022.We consider systems of rational agents who act and interact in pursuit of their individual and collective objectives. We study and formalise the reasoning of an agent, or of an external observer, about the expected choices of action of the other agents based on their objectives, in order to assess the reasoner’s ability, or expectation, to achieve their own objective. To formalize such reasoning we extend Pauly’s Coalition Logic with three new modal operators of conditional strategic reasoning, …Read more
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7Logic as a tool: a guide to formal logical reasoningWiley. 2016.Understanding propositional logic -- Deductive reasoning in propositional logic -- Understanding first-order logic -- Deductive reasoning in first-order logic -- Applications : mathematical proofs and automated reasoning -- Answers and solutions to selected exercises.
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4ForewordJournal of Applied Non-Classical Logics 21 (1): 7-8. 2011.This is an editorial foreword to the JANCL special issue on Logics for Multi-agent Systems.
Areas of Specialization
Science, Logic, and Mathematics |
Areas of Interest
Science, Logic, and Mathematics |