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Profile: Dov Gabbay
  1.  85 DLs
    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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  2.  71 DLs
    Dov M. Gabbay & Karl Schlechta (2009). Roadmap for Preferential Logics. Journal of Applied Non-Classical Logics 19 (1):43-95.
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  3.  64 DLs
    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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  4.  60 DLs
    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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  5.  57 DLs
    Dov Gabbay & George Metcalfe (2007). Fuzzy Logics Based on [0,1)-Continuous Uninorms. Archive for Mathematical Logic 46 (5-6):425-449.
    Axiomatizations are presented for fuzzy logics characterized by uninorms continuous on the half-open real unit interval [0,1), generalizing the continuous t-norm based approach of Hájek. Basic uninorm logic BUL is defined and completeness is established with respect to algebras with lattice reduct [0,1] whose monoid operations are uninorms continuous on [0,1). Several extensions of BUL are also introduced. In particular, Cross ratio logic CRL, is shown to be complete with respect to one special uninorm. A Gentzen-style hypersequent calculus is provided (...)
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  6.  52 DLs
    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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  7.  39 DLs
    George Metcalfe, Nicola Olivetti & Dov Gabbay (2004). Analytic Calculi for Product Logics. Archive for Mathematical Logic 43 (7):859-889.
    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.
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  8.  36 DLs
    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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  9.  34 DLs
    Dov Gabbay, Rolf Nossum & John Woods (2006). Context-Dependent Abduction and Relevance. Journal of Philosophical Logic 35 (1):65 - 81.
    Based on the premise that what is relevant, consistent, or true may change from context to context, a formal framework of relevance and context is proposed in which • contexts are mathematical entities • each context has its own language with relevant implication • the languages of distinct contexts are connected by embeddings • inter-context deduction is supported by bridge rules • databases are sets of formulae tagged with deductive histories and the contexts they belong to • abduction and revision (...)
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  10.  33 DLs
    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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  11.  32 DLs
    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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  12.  32 DLs
    Dov Gabbay, Stephan Hartmann & John Woods (eds.) (forthcoming). Handbook of the History and Philosophy of Logic, Vol. 10: Inductive Logic. Elsevier.
  13.  31 DLs
    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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  14.  27 DLs
    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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  15.  26 DLs
    Dov Gabbay & Franz Guenthner (eds.) (1989). Handbook of Philosophical Logic. Kluwer.
    The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work ...
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  16.  26 DLs
    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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  17.  25 DLs
    Dov Gabbay & Ruth Kempson (1996). Language and Proof Theory. Journal of Logic, Language and Information 5 (3-4):247-251.
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  18.  25 DLs
    Dov M. Gabbay (1977). Craig Interpolation Theorem for Intuitionistic Logic and Extensions Part III. Journal of Symbolic Logic 42 (2):269-271.
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  19.  22 DLs
    Dov Gabbay & John Woods (2006). Advice on Abductive Logic. Logic Journal of the Igpl 14 (2):189-219.
    One of our purposes here is to expose something of the elementary logical structure of abductive reasoning, and to do so in a way that helps orient theorists to the various tasks that a logic of abduction should concern itself with. We are mindful of criticisms that have been levelled against the very idea of a logic of abduction; so we think it prudent to proceed with a certain diffidence. That our own account of abduction is itself abductive is methodological (...)
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  20.  22 DLs
    Dov M. Gabbay & Karl Schlechta (2010). A Theory of Hierarchical Consequence and Conditionals. Journal of Logic, Language and Information 19 (1):3-32.
    We introduce -ranked preferential structures and combine them with an accessibility relation. -ranked preferential structures are intermediate between simple preferential structures and ranked structures. The additional accessibility relation allows us to consider only parts of the overall -ranked structure. This framework allows us to formalize contrary to duty obligations, and other pictures where we have a hierarchy of situations, and maybe not all are accessible to all possible worlds. Representation results are proved.
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  21.  21 DLs
    Dov M. Gabbay (ed.) (2002). Handbook of the Logic of Argument and Inference: The Turn Towards the Practical. Elsevier.
    The Handbook of the Logic of Argument and Inference is an authoritative reference work in a single volume, designed for the attention of senior undergraduates, graduate students and researchers in all the leading research areas concerned with the logic of practical argument and inference. After an introductory chapter, the role of standard logics is surveyed in two chapters. These chapters can serve as a mini-course for interested readers, in deductive and inductive logic, or as a refresher. Then follow two chapters (...)
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  22.  20 DLs
    Dov M. Gabbay & Andrzej Szałas (2009). Voting by Eliminating Quantifiers. Studia Logica 92 (3):365 - 379.
    Mathematical theory of voting and social choice has attracted much attention. In the general setting one can view social choice as a method of aggregating individual, often conflicting preferences and making a choice that is the best compromise. How preferences are expressed and what is the “best compromise” varies and heavily depends on a particular situation. The method we propose in this paper depends on expressing individual preferences of voters and specifying properties of the resulting ranking by means of first-order (...)
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  23.  19 DLs
    Marcelo Finger & Dov Gabbay (1996). Combining Temporal Logic Systems. Notre Dame Journal of Formal Logic 37 (2):204-232.
    This paper investigates modular combinations of temporal logic systems. Four combination methods are described and studied with respect to the transfer of logical properties from the component one-dimensional temporal logics to the resulting combined two-dimensional temporal logic. Three basic logical properties are analyzed, namely soundness, completeness, and decidability. Each combination method comprises three submethods that combine the languages, the inference systems, and the semantics of two one-dimensional temporal logic systems, generating families of two-dimensional temporal languages with varying expressivity and varying (...)
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  24.  18 DLs
    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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  25.  18 DLs
    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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  26.  17 DLs
    Stéphane Demri & Dov Gabbay (2000). On Modal Logics Characterized by Models with Relative Accessibility Relations: Part I. Studia Logica 65 (3):323-353.
    This work is divided in two papers (Part I and Part II). In Part I, we study a class of polymodal logics (herein called the class of "Rare-logics") for which the set of terms indexing the modal operators are hierarchized in two levels: the set of Boolean terms and the set of terms built upon the set of Boolean terms. By investigating different algebraic properties satisfied by the models of the Rare-logics, reductions for decidability are established by faithfully translating the (...)
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  27.  17 DLs
    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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  28.  17 DLs
    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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  29.  16 DLs
    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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  30.  16 DLs
    Dov M. Gabbay & Leendert van der Torre (2009). Preface for Studia Logica Special Issue (2). Studia Logica 93 (2-3):105-108.
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  31.  16 DLs
    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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  32.  16 DLs
    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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  33.  15 DLs
    Dov Gabbay & John Woods (2008). Resource-Origins of Nonmonotonicity. Studia Logica 88 (1):85 - 112.
    Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning from assumptions Δ to conclusions C without their being any deductive chain from Δ to C. Such jumps are done by various mechanisms which are strongly dependent on context and knowledge of how the actual world functions. Our aim is to motivate these jump rules as inference rules designed to optimise survival in an environment with scant resources of effort and time. (...)
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  34.  15 DLs
    Michael Abraham, Dov M. Gabbay, Gabriel Hazut, Yosef E. Maruvka & Uri Schild (2011). Logical Analysis of the Talmudic Rules of General and Specific (Klalim-U-Pratim). History and Philosophy of Logic 32 (1):47-62.
    This article deals with a set-theoretic interpretation of the Talmudic rules of General and Specific, known as Klal and Prat (KP), Prat and Klal (PK), Klal and Prat and Klal (KPK) and Prat and Klal and Prat (PKP).
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  35.  15 DLs
    Dov M. Gabbay (1977). On Some New Intuitionistic Propositional Connectives. I. Studia Logica 36 (1-2):127 - 139.
  36.  15 DLs
    Dov M. Gabbay & Nicola Olivetti (1998). Algorithmic Proof Methods and Cut Elimination for Implicational Logics Part I: Modal Implication. Studia Logica 61 (2):237-280.
    In this work we develop goal-directed deduction methods for the implicational fragment of several modal logics. We give sound and complete procedures for strict implication of K, T, K4, S4, K5, K45, KB, KTB, S5, G and for some intuitionistic variants. In order to achieve a uniform and concise presentation, we first develop our methods in the framework of Labelled Deductive Systems [Gabbay 96]. The proof systems we present are strongly analytical and satisfy a basic property of cut admissibility. We (...)
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  37.  15 DLs
    Dov Gabbay, Odinaldo Rodrigues & Alessandra Russo (2008). Belief Revision in Non-Classical Logics. Review of Symbolic Logic 1 (3):267-304.
    In this article, we propose a belief revision approach for families of (non-classical) logics whose semantics are first-order axiomatisable. Given any such (non-classical) logic , the approach enables the definition of belief revision operators for , in terms of a belief revision operation satisfying the postulates for revision theory proposed by Alchourrrdenfors and Makinson (AGM revision, Alchourrukasiewicz's many-valued logic. In addition, we present a general methodology to translate algebraic logics into classical logic. For the examples provided, we analyse in what (...)
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  38.  15 DLs
    Dov M. Gabbay (1972). A General Filtration Method for Modal Logics. Journal of Philosophical Logic 1 (1):29 - 34.
  39.  13 DLs
    Jochen Dörre, Esther König & Dov Gabbay (1996). Fibred Semantics for Feature-Based Grammar Logic. Journal of Logic, Language and Information 5 (3-4):387-422.
    This paper gives a simple method for providing categorial brands of feature-based unification grammars with a model-theoretic semantics. The key idea is to apply the paradigm of fibred semantics (or layered logics, see Gabbay (1990)) in order to combine the two components of a feature-based grammar logic. We demonstrate the method for the augmentation of Lambek categorial grammar with Kasper/Rounds-style feature logic. These are combined by replacing (or annotating) atomic formulas of the first logic, i.e. the basic syntactic types, by (...)
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  40.  13 DLs
    Dov M. Gabbay (1976). On Kreisel's Notion of Validity in Post Systems. Studia Logica 35 (3):285 - 295.
    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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  41.  13 DLs
    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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  42.  13 DLs
    Dov M. Gabbay & Ruy J. G. B. de Queiroz (1992). Extending the Curry-Howard Interpretation to Linear, Relevant and Other Resource Logics. Journal of Symbolic Logic 57 (4):1319-1365.
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  43.  13 DLs
    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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  44.  13 DLs
    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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  45.  12 DLs
    Dov M. Gabbay (1977). A New Version of Beth Semantics for Intuitionistic Logic. Journal of Symbolic Logic 42 (2):306-308.
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  46.  11 DLs
    Dov M. Gabbay (1974). A Generalization of the Concept of Intensional Semantics. Philosophia 4 (2-3):251-270.
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  47.  11 DLs
    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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  48.  11 DLs
    Dov Gabbay & John Woods (2001). Non-Cooperation in Dialogue Logic. Synthese 127 (1-2):161 - 186.
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  49.  11 DLs
    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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  50.  10 DLs
    Stéphane Demri & Dov Gabbay (2000). On Modal Logics Characterized by Models with Relative Accessibility Relations: Part II. Studia Logica 66 (3):349-384.
    This work is divided in two papers (Part I and Part II). In Part I, we introduced the class of Rare-logics for which the set of terms indexing the modal operators are hierarchized in two levels: the set of Boolean terms and the set of terms built upon the set of Boolean terms. By investigating different algebraic properties satisfied by the models of the Rare-logics, reductions for decidability were established by faithfully translating the Rare-logics into more standard modal logics (some (...)
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