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Profile: Dov Gabbay
  1.  19
    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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  2. Dov M. Gabbay, Ian Hodkinson & Mark Reynolds (1994). Temporal Logic Mathematical Foundations and Computational Aspects. Monograph Collection (Matt - Pseudo).
     
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  3.  46
    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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  4.  1
    Dov M. Gabbay (1986). Semantical Investigations in Heyting's Intuitionistic Logic. Journal of Symbolic Logic 51 (3):824-824.
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  5.  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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  6.  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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  7.  29
    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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  8.  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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  9.  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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  10.  18
    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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  11. 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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  12.  10
    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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  13.  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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  14.  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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  15.  3
    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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  16.  37
    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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  17.  30
    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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  18.  21
    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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  19. Dov M. Gabbay & Heinrich Wansing (2001). What Is Negation? Studia Logica 69 (3):435-439.
     
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  20.  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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  21.  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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  22.  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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  23. Samson Abramsky, Dov M. Gabbay & Thomas S. E. Maibaum (1992). Handbook of Logic in Computer Science. Monograph Collection (Matt - Pseudo).
     
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  24.  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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  25.  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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  26.  24
    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 (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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  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.  11
    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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  30.  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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  31.  11
    Dov M. Gabbay (1981). Expressive Functional Completeness in Tense Logic (Preliminary Report). In U. Mönnich (ed.), Aspects of Philosophical Logic. Dordrecht 91--117.
  32.  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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  33.  75
    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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  34. 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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  35.  73
    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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  36.  3
    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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  37. Dov M. Gabbay & John Woods (2003). Agenda Relevance - a Study in Formal Pragmatics. Monograph Collection (Matt - Pseudo).
     
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  38.  5
    Dov M. Gabbay (1970). The Decidability of the Kreisel-Putnam System. Journal of Symbolic Logic 35 (3):431-437.
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  39.  4
    Dov M. Gabbay (1975). Model Theory for Tense Logics. Annals of Mathematical Logic 8 (1-2):185-236.
  40.  17
    Dov M. Gabbay (1972). A General Theory of the Conditional in Terms of a Ternary Operator. Theoria 38 (3):97-104.
  41.  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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  42.  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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  43.  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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  44.  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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  45.  12
    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.
    The issue of representing access control requirements continues to demand significant attention. The focus of researchers has traditionally been on developing particular access control models and policy specification languages for particular applications. However, this approach has resulted in an unnecessary surfeit of models and languages. In contrast, we describe a general access control model and a logic-based specification language from which both existing and novel access control models may be derived as particular cases and from which several approaches can be (...)
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  46.  4
    Dov M. Gabbay & John Woods (2009). Fallacies as Cognitive Virtues. In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy. Springer Verlag 57--98.
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  47.  10
    Dov M. Gabbay & Andrzej Szałas (2009). Annotation Theories Over Finite Graphs. Studia Logica 93 (2/3):147 - 180.
    In the current paper we consider theories with vocabulary containing a number of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations represent unique annotations of the graph's nodes. Such theories, which we call annotation theories^ can be used in many applications, including the formalization of argumentation, approximate reasoning, semantics of logic programs, graph coloring, etc. We address a number of problems related to annotation theories over finite models, including satisfiability, querying problem, (...)
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  48.  6
    Dov M. Gabbay (1972). Sufficient Conditions for the Undecidability of Intuitionistic Theories with Applications. Journal of Symbolic Logic 37 (2):375-384.
  49.  25
    Marcello D'agostino, Dov M. Gabbay & Alessandra Russo (1997). Grafting Modalities Onto Substructural Implication Systems. Studia Logica 59 (1):65-102.
    We investigate the semantics of the logical systems obtained by introducing the modalities and into the family of substructural implication logics (including relevant, linear and intuitionistic implication). Then, in the spirit of the LDS (Labelled Deductive Systems) methodology, we "import" this semantics into the classical proof system KE. This leads to the formulation of a uniform labelled refutation system for the new logics which is a natural extension of a system for substructural implication developed by the first two authors in (...)
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  50.  46
    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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