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Dov Gabbay
Hebrew University of Jerusalem
  1.  67
    A Logical Account of Formal Argumentation.Martin W. A. Caminada & Dov M. Gabbay - 2009 - 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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  2. Analysis of the Talmudic Argumentum A Fortiori Inference Rule Using Matrix Abduction.M. Abraham, Dov M. Gabbay & U. Schild - 2009 - 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 $a_{i,j} = 1$ or $a_{i,j} =?$ undecided. This algorithmic method is then applied (...)
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  3.  38
    Labelled Deductive Systems.Dov M. Gabbay - 1996 - 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.  33
    Logical Modes of Attack in Argumentation Networks.Dov M. Gabbay & Artur S. D'Avila Garcez - 2009 - 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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  5.  7
    Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1986 - Journal of Symbolic Logic 51 (3):824-824.
  6. Temporal Logic Mathematical Foundations and Computational Aspects.Dov M. Gabbay, Ian Hodkinson & Mark Reynolds - 1994
     
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  7.  52
    Many-Dimensional Modal Logics: Theory and Applications.Dov M. Gabbay (ed.) - 2003 - 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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  8.  57
    An Irreflexivity Lemma with Applications to Axiomatizations of Conditions on Tense Frames.Dov M. Gabbay - 1981 - In U. Mönnich (ed.), Aspects of Philosophical Logic. Dordrecht. pp. 67--89.
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  9.  83
    Roadmap for Preferential Logics.Dov M. Gabbay & Karl Schlechta - 2009 - Journal of Applied Non-Classical Logics 19 (1):43-95.
  10.  33
    Semantics for Higher Level Attacks in Extended Argumentation Frames. Part 1: Overview.Dov M. Gabbay - 2009 - 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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  11.  18
    Reactive Preferential Structures and Nonmonotonic Consequence.Dov M. Gabbay & Karl Schlechta - 2009 - 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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  12.  29
    Philosophy of Economics.Uskali Mäki, Dov M. Gabbay, Paul Thagard & John Woods (eds.) - 2012 - 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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  13.  47
    Adding a Temporal Dimension to a Logic System.Marcelo Finger & Dov M. Gabbay - 1992 - 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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  14.  17
    Meta-Argumentation Modelling I: Methodology and Techniques.Guido Boella, Dov M. Gabbay, Leendert van der Torre & Serena Villata - 2009 - Studia Logica 93 (2-3):297 - 355.
    In this paper, we introduce the methodology and techniques of metaargumentation to model argumentation. The methodology of meta-argumentation instantiates Dung's abstract argumentation theory with an extended argumentation theory, and is thus based on a combination of the methodology of instantiating abstract arguments, and the methodology of extending Dung's basic argumentation frameworks with other relations among abstract arguments. The technique of meta-argumentation applies Dung's theory of abstract argumentation to itself, by instantiating Dung's abstract arguments with meta-arguments using a technique called flattening. (...)
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  15.  34
    Size and Logic.Dov M. Gabbay & Karl Schlechta - 2009 - 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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  16.  8
    Goal-Directed Proof Theory.Dov M. Gabbay - 2000 - 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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  17.  13
    Dung's Argumentation is Essentially Equivalent to Classical Propositional Logic with the Peirce–Quine Dagger.Dov M. Gabbay - 2011 - Logica Universalis 5 (2):255-318.
    In this paper we show that some versions of Dung’s abstract argumentation frames are equivalent to classical propositional logic. In fact, Dung’s attack relation is none other than the generalised Peirce–Quine dagger connective of classical logic which can generate the other connectives ${\neg, \wedge, \vee, \to}$ of classical logic. After establishing the above correspondence we offer variations of the Dung argumentation frames in parallel to variations of classical logic, such as resource logics, predicate logic, etc., etc., and create resource argumentation (...)
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  18.  4
    Fibred Security Language.Guido Boella, Dov M. Gabbay, Valerio Genovese & Leendert Van Der Torre - 2009 - 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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  19. Abductive Reasoning in Neural-Symbolic Systems.Artur S. D’Avila Garcez, Dov M. Gabbay, Oliver Ray & John Woods - 2007 - 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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  20. What Is Negation?Dov M. Gabbay & Heinrich Wansing - 2001 - Studia Logica 69 (3):435-439.
  21.  43
    Two Dimensional Standard Deontic Logic [Including a Detailed Analysis of the 1985 Jones–Pörn Deontic Logic System].Mathijs Boer, Dov M. Gabbay, Xavier Parent & Marija Slavkovic - 2012 - 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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  22.  6
    Investigations in Modal and Tense Logics with Application to Problems in Philosophy and Linguistics.Dov M. Gabbay - 1979 - Journal of Symbolic Logic 44 (4):656-657.
  23.  35
    Second-Order Quantifier Elimination in Higher-Order Contexts with Applications to the Semantical Analysis of Conditionals.Dov M. Gabbay & Andrzej Szałas - 2007 - 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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  24.  27
    Two Dimensional Standard Deontic Logic [Including a Detailed Analysis of the 1985 Jones–Pörn Deontic Logic System].Mathijs de Boer, Dov M. Gabbay, Xavier Parent & Marija Slavkovic - 2012 - 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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  25.  24
    Fibred Security Language.Guido Boella, Dov M. Gabbay, Valerio Genovese & Leendert van der Torre - 2009 - 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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  26. Handbook of Logic in Computer Science.Samson Abramsky, Dov M. Gabbay & Thomas S. E. Maibaum - 1992
     
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  27.  7
    Handbook of Logic in Artificial Intelligence and Logic Programming, Volume 3, Nonmonotonic Reasoning and Uncertain Reasoning.Dov M. Gabbay, C. J. Hogger, J. A. Robinson & D. Nute - 2000 - Bulletin of Symbolic Logic 6 (4):480-484.
  28.  14
    Fibring Logics.Dov M. Gabbay - 1999 - 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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  29.  17
    Expressive Functional Completeness in Tense Logic (Preliminary Report).Dov M. Gabbay - 1981 - In U. Mönnich (ed.), Aspects of Philosophical Logic. Dordrecht. pp. 91--117.
  30. Fibring Logics.Dov M. Gabbay - 2000 - Studia Logica 66 (3):440-443.
     
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  31.  38
    What is a Logical System?Dov M. Gabbay (ed.) - 1994 - 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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  32.  11
    Semantic Interpolation.Dov M. Gabbay & Karl Schlechta - 2010 - Journal of Applied Non-Classical Logics 20 (4):345-371.
  33.  6
    A Neural Cognitive Model of Argumentation with Application to Legal Inference and Decision Making.Artur S. D'Avila Garcez, Dov M. Gabbay & Luis C. Lamb - 2014 - Journal of Applied Logic 12 (2):109-127.
    Formal models of argumentation have been investigated in several areas, from multi-agent systems and artificial intelligence (AI) to decision making, philosophy and law. In artificial intelligence, logic-based models have been the standard for the representation of argumentative reasoning. More recently, the standard logic-based models have been shown equivalent to standard connectionist models. This has created a new line of research where (i) neural networks can be used as a parallel computational model for argumentation and (ii) neural networks can be used (...)
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  34.  7
    Model Theory for Tense Logics.Dov M. Gabbay - 1975 - Annals of Mathematical Logic 8 (1-2):185-236.
  35. Handbook of Logic in Artificial Intelligence and Logic Programming.Dov M. Gabbay, Christopher John Hogger & J. A. Robinson - 1993
     
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  36.  72
    Independence — Revision and Defaults.Dov M. Gabbay & Karl Schlechta - 2009 - 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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  37.  50
    A General Theory of the Conditional in Terms of a Ternary Operator.Dov M. Gabbay - 1972 - Theoria 38 (3):97-104.
  38. Handbook of the History of Logic.Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.) - 2004 - 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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  39.  5
    The Decidability of the Kreisel-Putnam System.Dov M. Gabbay - 1970 - Journal of Symbolic Logic 35 (3):431-437.
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  40. Agenda Relevance - a Study in Formal Pragmatics.Dov M. Gabbay & John Woods - 2003
     
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  41.  5
    Cumulativity Without Closure of the Domain Under Finite Unions.Dov M. Gabbay & Karl Schlechta - 2008 - Review of Symbolic Logic 1 (3):372-392.
    For nonmonotonic logics, Cumulativity is an important logical rule. We show here that Cumulativity fans out into an infinity of different conditions, if the domain is not closed under finite unions.
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  42.  50
    A General Theory of Structured Consequence Relations.Dov M. Gabbay - 1995 - 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.  9
    Sufficient Conditions for the Undecidability of Intuitionistic Theories with Applications.Dov M. Gabbay - 1972 - Journal of Symbolic Logic 37 (2):375-384.
  44.  11
    Semantics for Higher Level Attacks in Extended Argumentation Frames Part 1: Overview.Dov M. Gabbay - 2009 - 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 to such networks. We offer three different approaches to obtaining semantics. 1. The translation approach (...)
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  45.  48
    Grafting Modalities Onto Substructural Implication Systems.Marcello D'agostino, Dov M. Gabbay & Alessandra Russo - 1997 - 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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  46.  19
    On Some New Intuitionistic Propositional Connectives. I.Dov M. Gabbay - 1977 - Studia Logica 36 (1-2):127 - 139.
  47.  26
    Extending the Curry-Howard Interpretation to Linear, Relevant and Other Resource Logics.Dov M. Gabbay & Ruy J. G. B. de Queiroz - 1992 - Journal of Symbolic Logic 57 (4):1319-1365.
  48.  9
    Fallacies as Cognitive Virtues.Dov M. Gabbay & John Woods - 2009 - In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy. Springer Verlag. pp. 57--98.
  49.  35
    A Comment on Work by Booth and Co-Authors.Dov M. Gabbay & Karl Schlechta - 2010 - Studia Logica 94 (3):403-432.
    Booth and his co-authors have shown in [2], that many new approaches to theory revision (with fixed K ) can be represented by two relations, , where is a sub-relation of < . They have, however, left open a characterization of the infinite case, which we treat here.
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  50.  23
    Montague Type Semantics for Modal Logics with Propositional Quantifiers.Dov M. Gabbay - 1971 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 17 (1):245-249.
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