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15REVIEWS-Handbook of philosophical logic, vol. 10Bulletin of Symbolic Logic 13 (2): 248-250. 2007.
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23A 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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67Naming 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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49Undecidability 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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52Fibred 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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109Neural-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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26Compiled 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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122Roadmap for preferential logicsJournal of Applied Non-Classical Logics 19 (1): 43-95. 2009.We give a systematic overview of semantical and logical rules in non monotonic and related logics. We show connections and sometimes subtle differences, and also compare such rules to uses of the notion of size.
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34A new version of Beth semantics for intuitionistic logicJournal of Symbolic Logic 42 (2): 306-308. 1977.
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101What is a logical system? (edited book)Oxford University Press. 1994.This superb collection of papers focuses on a fundamental question in logic and computation: What is a logical system? With contributions from leading researchers--including Ian Hacking, Robert Kowalski, Jim Lambek, Neil Tennent, Arnon Avron, L. Farinas del Cerro, Kosta Dosen, and Solomon Feferman--the book presents a wide range of views on how to answer such a question, reflecting current, mainstream approaches to logic and its applications. Written to appeal to a diverse audience of readers, W…Read more
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16Fibred Security LanguageStudia Logica 92 (3). 2009.We study access control policies based on the says operator by introducing a logical framework called Fibred Security Language (FSL) which is able to deal with features like joint responsibility between sets of principals and to identify them by means of first-order formulas. FSL is based on a multimodal logic methodology. We first discuss the main contributions from the expressiveness point of view, we give semantics for the language (both for classical and intuitionistic fragment), we then pro…Read more
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34On Kreisel's notion of validity in post systemsStudia Logica 35 (3). 1976.This paper investigates various interpretations of HPC (Heyting's predicate calculus) and mainly of HPC0 (Heyting's propositional calculus) in Post systems.§1 recalls some background material concerning HPC including the Kripke and Beth interpretations, and later sections study the various interpretations available.
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43Temporal Logic: Mathematical Foundations and Computational AspectsOxford University Press on Demand. 1994.This much-needed book provides a thorough account of temporal logic, one of the most important areas of logic in computer science today. The book begins with a solid introduction to semantical and axiomatic approaches to temporal logic. It goes on to cover predicate temporal logic, meta-languages, general theories of axiomatization, many dimensional systems, propositional quantifiers, expressive power, Henkin dimension, temporalization of other logics, and decidability results. With its inclusio…Read more
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60Extending the Curry-Howard interpretation to linear, relevant and other resource logicsJournal of Symbolic Logic 57 (4): 1319-1365. 1992.
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14KM99] GP Kogan and JA Makowsky. Computing Schur functions for Borchardt matrices. in preparation, 1999. Kog96] GP Kogan. Computing the permanent over elds of characteristic 3: Where and why it becomes dificult. In FOCS'96, pages 108 {114. IEEE, 1996 (review)Annals of Pure and Applied Logic 78 (2): 189-202. 1996.
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26Modal Logics of Reactive FramesStudia Logica 93 (2-3): 405-446. 2009.A reactive graph generalizes the concept of a graph by making it dynamic, in the sense that the arrows coming out from a point depend on how we got there. This idea was first applied to Kripke semantics of modal logic in [2]. In this paper we strengthen that unimodal language by adding a second operator. One operator corresponds to the dynamics relation and the other one relates paths with the same endpoint. We explore the expressivity of this interpretation by axiomatizing some natural subclass…Read more
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71Cut and payJournal of Logic, Language and Information 15 (3): 195-218. 2006.In this paper we study families of resource aware logics that explore resource restriction on rules; in particular, we study the use of controlled cut-rule and introduce three families of parameterised logics that arise from different ways of controlling the use of cut. We start with a formulation of classical logic in which cut is non-eliminable and then impose restrictions on the use of cut. Three Cut-and-Pay families of logics are presented, and it is shown that each family provides an approx…Read more
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57Two dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones–Pörn deontic logic system]Synthese 187 (2): 623-660. 2012.This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a detailed case study i…Read more
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40Semantics for Higher Level Attacks in Extended Argumentation Frames Part 1: OverviewStudia Logica 93 (2-3): 357-381. 2009.In 2005 the author introduced networks which allow attacks on attacks of any level. So if a → b reads a attacks 6, then this attack can itself be attacked by another node c. This attack itself can attack another node d. This situation can be iterated to any level with attacks and nodes attacking other attacks and other nodes. In this paper we provide semantics to such networks. We offer three different approaches to obtaining semantics. 1. The translation approach This uses the methodology of ' …Read more
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37Completeness properties of heyting's predicate calculus with respect to re modelsJournal of Symbolic Logic 41 (1): 81-94. 1976.
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61Analytic Calculi for Product LogicsArchive for Mathematical Logic 43 (7): 859-889. 2004.Product logic Π is an important t-norm based fuzzy logic with conjunction interpreted as multiplication on the real unit interval [0,1], while Cancellative hoop logic CHL is a related logic with connectives interpreted as for Π but on the real unit interval with 0 removed (0,1]. Here we present several analytic proof systems for Π and CHL, including hypersequent calculi, co-NP labelled calculi and sequent calculi.