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Profile: Dov Gabbay
  1.  78
    Dov M. Gabbay & Karl Schlechta (2009). Roadmap for Preferential Logics. Journal of Applied Non-Classical Logics 19 (1):43-95.
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  2. Artur S. D’Avila Garcez, Dov M. Gabbay, Oliver Ray & John Woods (2007). Abductive Reasoning in Neural-Symbolic Systems. Topoi 26 (1):37-49.
    Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abduction. We are interested in benefiting from developments (...)
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  3.  22
    Dov M. Gabbay (1996). Labelled Deductive Systems. Oxford University Press.
    This important book provides a new unifying methodology for logic. It replaces the traditional view of logic as manipulating sets of formulas with the notion of structured families of labelled formulas with algebraic structures. This approach has far reaching consequences for the methodology of logics and their semantics, and the book studies the main features of such systems along with their applications. It will interest logicians, computer scientists, philosophers and linguists.
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  4. Dov M. Gabbay, Ian Hodkinson & Mark Reynolds (1994). Temporal Logic Mathematical Foundations and Computational Aspects. Monograph Collection (Matt - Pseudo).
     
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  5.  43
    Dov M. Gabbay (1981). An Irreflexivity Lemma with Applications to Axiomatizations of Conditions on Tense Frames. In U. Mönnich (ed.), Aspects of Philosophical Logic. Dordrecht 67--89.
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  6.  47
    Dov M. Gabbay (ed.) (2003). Many-Dimensional Modal Logics: Theory and Applications. Elsevier North Holland.
    Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects. To study (...)
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  7.  1
    Dov M. Gabbay (1986). Semantical Investigations in Heyting's Intuitionistic Logic. Journal of Symbolic Logic 51 (3):824-824.
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  8.  20
    Martin W. A. Caminada & Dov M. Gabbay (2009). A Logical Account of Formal Argumentation. Studia Logica 93 (2-3):109-145.
    In the current paper, we re-examine how abstract argumentation can be formulated in terms of labellings, and how the resulting theory can be applied in the field of modal logic. In particular, we are able to express the extensions of an argumentation framework as models of a set of modal logic formulas that represents the argumentation framework. Using this approach, it becomes possible to define the grounded extension in terms of modal logic entailment.
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  9.  30
    Dov M. Gabbay (2009). Fibring Argumentation Frames. Studia Logica 93 (2/3):231 - 295.
    This paper is part of a research program centered around argumentation networks and offering several research directions for argumentation networks, with a view of using such networks for integrating logics and network reasoning. In Section 1 we introduce our program manifesto. In Section 2 we motivate and show how to substitute one argumentation network as a node in another argumentation network. Substitution is a purely logical operation and doing it for networks, besides developing their theory further, also helps us see (...)
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  10.  26
    Dov M. Gabbay (2009). Modal Provability Foundations for Argumentation Networks. Studia Logica 93 (2/3):181 - 198.
    Given an argumentation network we associate with it a modal formula representing the 'logical content' of the network. We show a one-to-one correspondence between all possible complete Caminada labellings of the network and all possible models of the formula.
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  11.  11
    Dov M. Gabbay & Artur S. D'Avila Garcez (2009). Logical Modes of Attack in Argumentation Networks. Studia Logica 93 (2-3):199-230.
    This paper studies methodologically robust options for giving logical contents to nodes in abstract argumentation networks. It defines a variety of notions of attack in terms of the logical contents of the nodes in a network. General properties of logics are refined both in the object level and in the metalevel to suit the needs of the application. The network-based system improves upon some of the attempts in the literature to define attacks in terms of defeasible proofs, the so-called rule-based (...)
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  12.  23
    Dov M. Gabbay (2009). Semantics for Higher Level Attacks in Extended Argumentation Frames. Part 1: Overview. Studia Logica 93 (2/3):357 - 381.
    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 (of extensions) to such networks. We offer three different approaches to obtaining semantics. 1. The (...)
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  13.  19
    Uskali Mäki, Dov M. Gabbay, Paul Thagard & John Woods (eds.) (2012). Philosophy of Economics. North Holland.
    This volume serves as a detailed introduction for those new to the field as well as a rich source of new insights and potential research agendas for those already engaged with the philosophy of economics.
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  14.  19
    Yining Wu, Martin Caminada & Dov M. Gabbay (2009). Complete Extensions in Argumentation Coincide with 3-Valued Stable Models in Logic Programming. Studia Logica 93 (2/3):383 - 403.
    In this paper, we prove the correspondence between complete extensions in abstract argumentation and 3-valued stable models in logic programming. This result is in line with earlier work of [6] that identified the correspondence between the grounded extension in abstract argumentation and the well-founded model in logic programming, as well as between the stable extensions in abstract argumentation and the stable models in logic programming.
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  15.  38
    Martin W. A. Caminada & Dov M. Gabbay (2009). A Logical Account of Formal Argumentation. Studia Logica 93 (2/3):109 - 145.
    In the current paper, we re-examine how abstract argumentation can be formulated in terms of labellings, and how the resulting theory can be applied in the field of modal logic. In particular, we are able to express the (complete) extensions of an argumentation framework as models of a set of modal logic formulas that represents the argumentation framework. Using this approach, it becomes possible to define the grounded extension in terms of modal logic entailment.
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  16.  31
    Dov M. Gabbay & Sérgio Marcelino (2009). Modal Logics of Reactive Frames. Studia Logica 93 (2/3):405 - 446.
    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 (...)
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  17.  14
    Dov M. Gabbay & Artur S. D’Avila Garcez (2009). Logical Modes of Attack in Argumentation Networks. Studia Logica 93 (2/3):199 - 230.
    This paper studies methodologically robust options for giving logical contents to nodes in abstract argumentation networks. It defines a variety of notions of attack in terms of the logical contents of the nodes in a network. General properties of logics are refined both in the object level and in the metalevel to suit the needs of the application. The network-based system improves upon some of the attempts in the literature to define attacks in terms of defeasible proofs, the so-called rule-based (...)
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  18.  14
    Dov M. Gabbay & Karl Schlechta (2009). Reactive Preferential Structures and Nonmonotonic Consequence. Review of Symbolic Logic 2 (2):414-450.
    We introduce Information Bearing Relation Systems (IBRS) as an abstraction of many logical systems. These are networks with arrows recursively leading to other arrows etc. We then define a general semantics for IBRS, and show that a special case of IBRS generalizes in a very natural way preferential semantics and solves open representation problems for weak logical systems. This is possible, as we can the strong coherence properties of preferential structures by higher arrows, that is, arrows, which do not go (...)
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  19.  4
    Guido Boella, Dov M. Gabbay, Valerio Genovese & Leendert Van Der Torre (2009). Fibred Security Language. Studia Logica 92 (3):395 - 436.
    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 prove that in order (...)
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  20.  34
    Marcelo Finger & Dov M. Gabbay (1992). Adding a Temporal Dimension to a Logic System. Journal of Logic, Language and Information 1 (3):203-233.
    We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with Since and Until) in a special way. We refer to this method as adding a temporal dimension to L or just temporalising L. We show that the logic system T(L) preserves several properties of the original temporal logic (...)
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  21.  77
    M. Abraham, Dov M. Gabbay & U. Schild (2009). Analysis of the Talmudic Argumentum a Fortiori Inference Rule (Kal Vachomer) Using Matrix Abduction. Studia Logica 92 (3):281 - 364.
    We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix with entries in {0, 1}, we allow for one or more blank squares in the matrix, say a i , j =?. The method allows us to decide whether to declare a i , j = 0 or a i , j = 1 (...)
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  22.  18
    Dov M. Gabbay & Karl Schlechta (2009). Size and Logic. Review of Symbolic Logic 2 (2):396-413.
    We show how to develop a multitude of rules of nonmonotonic logic from very simple and natural notions of size, using them as building blocks.
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  23.  4
    Dov M. Gabbay (2000). Goal-Directed Proof Theory. Kluwer Academic.
    Goal Directed Proof Theory presents a uniform and coherent methodology for automated deduction in non-classical logics, the relevance of which to computer science is now widely acknowledged. The methodology is based on goal-directed provability. It is a generalization of the logic programming style of deduction, and it is particularly favourable for proof search. The methodology is applied for the first time in a uniform way to a wide range of non-classical systems, covering intuitionistic, intermediate, modal and substructural logics. The book (...)
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  24.  12
    Guido Boella, Dov M. Gabbay, Valerio Genovese & Leendert van der Torre (2009). Fibred Security Language. Studia Logica 92 (3):395-436.
    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 prove that in order (...)
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  25.  13
    Dov M. Gabbay (1981). Expressive Functional Completeness in Tense Logic (Preliminary Report). In U. Mönnich (ed.), Aspects of Philosophical Logic. Dordrecht 91--117.
  26.  25
    Dov M. Gabbay & Andrzej Szałas (2007). Second-Order Quantifier Elimination in Higher-Order Contexts with Applications to the Semantical Analysis of Conditionals. Studia Logica 87 (1):37 - 50.
    Second-order quantifier elimination in the context of classical logic emerged as a powerful technique in many applications, including the correspondence theory, relational databases, deductive and knowledge databases, knowledge representation, commonsense reasoning and approximate reasoning. In the current paper we first generalize the result of Nonnengart and Szałas [17] by allowing second-order variables to appear within higher-order contexts. Then we focus on a semantical analysis of conditionals, using the introduced technique and Gabbay’s semantics provided in [10] and substantially using a third-order (...)
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  27. Dov M. Gabbay & Heinrich Wansing (2001). What Is Negation? Studia Logica 69 (3):435-439.
     
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  28.  5
    Dov M. Gabbay & Karl Schlechta (2010). Semantic Interpolation. Journal of Applied Non-Classical Logics 20 (4):345-371.
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  29. Samson Abramsky, Dov M. Gabbay & Thomas S. E. Maibaum (1992). Handbook of Logic in Computer Science. Monograph Collection (Matt - Pseudo).
     
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  30.  49
    Alexander Bochman & Dov M. Gabbay (2012). Sequential Dynamic Logic. Journal of Logic, Language and Information 21 (3):279-298.
    We introduce a substructural propositional calculus of Sequential Dynamic Logic that subsumes a propositional part of dynamic predicate logic, and is shown to be expressively equivalent to propositional dynamic logic. Completeness of the calculus with respect to the intended relational semantics is established.
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  31.  18
    Dov M. Gabbay (1972). A General Theory of the Conditional in Terms of a Ternary Operator. Theoria 38 (3):97-104.
  32.  9
    Dov M. Gabbay (1999). Fibring Logics. Clarendon Press.
    Modern applications of logic in mathematics, computer science, and linguistics use combined systems of different types of logic working together. This book develops a method for combining--or fibring--systems by breaking them into simple components which can be manipulated easily and recombined.
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  33. Dov M. Gabbay (1979). Investigations in Modal and Tense Logics with Application to Problems in Philosophy and Linguistics. Journal of Symbolic Logic 44 (4):656-657.
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  34.  29
    Dov M. Gabbay (1995). A General Theory of Structured Consequence Relations. Theoria 10 (2):49-78.
    There are several areas in logic where the monotonicity of the consequence relation fails to hold. Roughly these are the traditional non-monotonic systems arising in Artificial Intelligence (such as defeasible logics, circumscription, defaults, ete), numerical non-monotonic systems (probabilistic systems, fuzzy logics, belief functions), resource logics (also called substructural logics such as relevance logic, linear logic, Lambek calculus), and the logic of theory change (also called belief revision, see Alchourron, Gärdenfors, Makinson [2224]). We are seeking a common axiomatic and semantical approach (...)
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  35.  65
    Dov M. Gabbay & Karl Schlechta (2009). Independence — Revision and Defaults. Studia Logica 92 (3):381 - 394.
    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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  36.  11
    Mathijs Boer, Dov M. Gabbay, Xavier Parent & Marija Slavkovic (2012). Two Dimensional Standard Deontic Logic [Including a Detailed Analysis of the 1985 Jones–Pörn Deontic Logic System]. Synthese 187 (2):623-660.
    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 (...)
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  37.  1
    Dov M. Gabbay, C. J. Hogger, J. A. Robinson & D. Nute (2000). Handbook of Logic in Artificial Intelligence and Logic Programming, Volume 3, Nonmonotonic Reasoning and Uncertain Reasoning. Bulletin of Symbolic Logic 6 (4):480-484.
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  38.  4
    Mathijs de Boer, Dov M. Gabbay, Xavier Parent & Marija Slavkovic (2012). Two Dimensional Standard Deontic Logic [Including a Detailed Analysis of the 1985 Jones–Pörn Deontic Logic System]. Synthese 187 (2):623-660.
    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 (...)
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  39.  4
    Dov M. Gabbay (1974). A Normal Logic That is Complete for Neighborhood Frames but Not for Kripke Frames. Theoria 40 (3):148-153.
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  40.  4
    Dov M. Gabbay (1971). Montague Type Semantics for Modal Logics with Propositional Quantifiers. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 17 (1):245-249.
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  41.  4
    Dov M. Gabbay (1975). Model Theory for Tense Logics. Annals of Mathematical Logic 8 (1-2):185-236.
  42.  2
    Steve Barker, Guido Boella, Dov M. Gabbay & Valerio Genovese (2009). A Meta-Model of Access Control in a Fibred Security Language. Studia Logica 92 (3):437-477.
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  43.  29
    Dov M. Gabbay (ed.) (1994). What is a Logical System? Oxford University Press.
    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, What is a Logical System? will (...)
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  44. Dov M. Gabbay, Christopher John Hogger & J. A. Robinson (1993). Handbook of Logic in Artificial Intelligence and Logic Programming. Monograph Collection (Matt - Pseudo).
     
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  45.  74
    Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.) (2004). Handbook of the History of Logic. Elsevier.
    Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Gödel, The Emergence of Classical Logic, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, including Mediaeval and (...)
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  46.  5
    Dov M. Gabbay (1970). The Decidability of the Kreisel-Putnam System. Journal of Symbolic Logic 35 (3):431-437.
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  47.  3
    Dov M. Gabbay (1972). Model Theory for Intuitionistic Logic. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (4-6):49-54.
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  48. Dov M. Gabbay (2006). Guido Boella Dov M. Gabbay Leendert van der Torre Serena Villata. Studia Logica 82:1-59.
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  49.  36
    Dov M. Gabbay & Moshe Koppel (2011). Uncertainty Rules in Talmudic Reasoning. History and Philosophy of Logic 32 (1):63-69.
    The Babylonian Talmud, compiled from the 2nd to 7th centuries C.E., is the primary source for all subsequent Jewish laws. It is not written in apodeictic style, but rather as a discursive record of (real or imagined) legal (and other) arguments crossing a wide range of technical topics. Thus, it is not a simple matter to infer general methodological principles underlying the Talmudic approach to legal reasoning. Nevertheless, in this article, we propose a general principle that we believe helps to (...)
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  50. Dov M. Gabbay & John Woods (2003). Agenda Relevance - a Study in Formal Pragmatics. Monograph Collection (Matt - Pseudo).
     
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