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Dov Gabbay
Hebrew University of Jerusalem
  1.  58
    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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  2.  50
    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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  3. 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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  4. Temporal Logic Mathematical Foundations and Computational Aspects.Dov M. Gabbay, Ian Hodkinson & Mark Reynolds - 1994
     
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  5.  19
    Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1986 - Journal of Symbolic Logic 51 (3):824-824.
  6.  65
    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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  7.  84
    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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  8.  47
    Fibring Argumentation Frames.Dov M. Gabbay - 2009 - Studia Logica 93 (2):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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  9.  49
    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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  10.  56
    Handbook of Philosophical Logic.Dov M. Gabbay & Franz Guenthner (eds.) - 1989 - Kluwer Academic Publishers.
    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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  11. 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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  12.  42
    Complete Extensions in Argumentation Coincide with 3-Valued Stable Models in Logic Programming.Yining Wu, Martin Caminada & Dov M. Gabbay - 2009 - Studia Logica 93 (2):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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  13.  67
    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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  14.  13
    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.
  15. Roadmap for Preferential Logics.Dov M. Gabbay & Karl Schlechta - 2009 - Journal of Applied Non-Classical Logics 19 (1):43-95.
    We give a systematic overview of semantical and logical rules in non monotonic and related logics. We show connections and sometimes subtle differences, and also compare such rules to uses of the notion of size.
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  16.  22
    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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  17.  38
    Modal Provability Foundations for Argumentation Networks.Dov M. Gabbay - 2009 - Studia Logica 93 (2):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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  18.  22
    Model Theory for Tense Logics.Dov M. Gabbay - 1975 - Annals of Mathematical Logic 8 (1):185.
  19.  67
    A General Theory of the Conditional in Terms of a Ternary Operator.Dov M. Gabbay - 1972 - Theoria 38 (3):97-104.
  20.  40
    Handbook of the Logic of Argument and Inference: The Turn Towards the Practical.Dov M. Gabbay (ed.) - 2002 - 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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  21.  24
    Expressive Functional Completeness in Tense Logic (Preliminary Report).Dov M. Gabbay - 1981 - In U. Mönnich (ed.), Aspects of Philosophical Logic. Dordrecht. pp. 91--117.
  22.  21
    The Talmudic Logic Project, Ongoing Since 2008.Dov M. Gabbay, Uri Schild & Esther David - 2019 - Logica Universalis 13 (4):425-442.
    We describe the state of the Talmudic Logic project as of end of 2019. The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components centuries ahead of their time. In many cases the basic principles are not explicitly formulated, which makes it difficult to formalize and make available to the modern student of Logic. This project on Talmudic Logic, aims to present logical analysis of Talmudic reasoning using modern logical tools. (...)
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  23.  48
    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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  24.  19
    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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  25.  24
    Applications of Trees to Intermediate Logics.Dov M. Gabbay - 1972 - Journal of Symbolic Logic 37 (1):135-138.
  26.  38
    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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  27.  57
    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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  28.  13
    The Decidability of the Kreisel-Putnam System.Dov M. Gabbay - 1970 - Journal of Symbolic Logic 35 (3):431-437.
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  29.  33
    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.
  30.  55
    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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  31.  11
    A Practical Logic of Cognitive Systems.Dov M. Gabbay - 2003 - North Holland.
    Agenda Relevance is the first volume in the authors' omnibus investigation of the logic of practical reasoning, under the collective title, A Practical Logic of Cognitive Systems. In this highly original approach, practical reasoning is identified as reasoning performed with comparatively few cognitive assets, including resources such as information, time and computational capacity. Unlike what is proposed in optimization models of human cognition, a practical reasoner lacks perfect information, boundless time and unconstrained access to computational complexity. The practical reasoner is (...)
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  32.  45
    Modal Logics of Reactive Frames.Dov M. Gabbay & Sérgio Marcelino - 2009 - Studia Logica 93 (2):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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  33.  24
    On Some New Intuitionistic Propositional Connectives. I.Dov M. Gabbay - 1977 - Studia Logica 36 (1-2):127 - 139.
  34.  23
    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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  35.  9
    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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  36.  8
    Decidability Results in Non-Classical Logics. Part I.Dov M. Gabbay - 1975 - Annals of Mathematical Logic 8 (3):237.
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  37.  35
    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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  38.  26
    Annotation Theories Over Finite Graphs.Dov M. Gabbay & Andrzej Szałas - 2009 - Studia Logica 93 (2):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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  39.  27
    Sufficient Conditions for the Undecidability of Intuitionistic Theories with Applications.Dov M. Gabbay - 1972 - Journal of Symbolic Logic 37 (2):375-384.
  40.  37
    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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  41.  3
    Logic and Cognition.H. Cowles, Matthew Walenski, Robert Kluender, Markus Knauff, Artur S. Davila Garcez, Dov M. Gabbay, Oliver Ray, John Woods, Robin Clark & Murray Grossman - 2007 - Topoi 26 (1):51-62.
    We consider connections between number sense—the ability to judge number—and the interpretation of natural language quantifiers. In particular, we present empirical evidence concerning the neuroanatomical underpinnings of number sense and quantifier interpretation. We show, further, that impairment of number sense in patients can result in the impairment of the ability to interpret sentences containing quantifiers. This result demonstrates that number sense supports some aspects of the language faculty.
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  42.  46
    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.
  43.  18
    Model Theory for Intuitionistic Logic.Dov M. Gabbay - 1972 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (4-6):49-54.
  44.  14
    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.
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  45.  46
    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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  46.  9
    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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  47.  58
    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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  48.  43
    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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  49.  15
    Tense Systems with Discrete Moments of Time, Part I.Dov M. Gabbay - 1972 - Journal of Philosophical Logic 1 (1):35 - 44.
  50.  30
    Decidability of Some Intuitionistic Predicate Theories.Dov M. Gabbay - 1972 - Journal of Symbolic Logic 37 (3):579-587.
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