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Dov Gabbay
Hebrew University of Jerusalem
  1.  59
    Labelled deductive systems.Dov M. Gabbay - 1996 - New York: 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.  84
    Many-dimensional modal logics: theory and applications.Dov M. Gabbay (ed.) - 2003 - Boston: 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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  3.  36
    Temporal Logic: Mathematical Foundations and Computational Aspects.Dov M. Gabbay, Ian Hodkinson & Mark A. Reynolds - 1994 - Oxford University Press on Demand.
    This much-needed book provides a thorough account of temporal logic, one of the most important areas of logic in computer science today. The book begins with a solid introduction to semantical and axiomatic approaches to temporal logic. It goes on to cover predicate temporal logic, meta-languages, general theories of axiomatization, many dimensional systems, propositional quantifiers, expressive power, Henkin dimension, temporalization of other logics, and decidability results. With its inclusion of cutting-edge results and unifying methodologies, this book is an indispensable reference (...)
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  4. 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 (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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  5.  29
    Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1986 - Journal of Symbolic Logic 51 (3):824-824.
  6.  4
    Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1981 - Dordrecht, Netherland: Reidel.
    From the point of view of non-classical logics, Heyting's implication is the smallest implication for which the deduction theorem holds. This book studies properties of logical systems having some of the classical connectives and implication in the neighbourhood of Heyt ing's implication. I have not included anything on entailment, al though it belongs to this neighbourhood, mainly because of the appearance of the Anderson-Belnap book on entailment. In the later chapters of this book, I have included material that might be (...)
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  7.  75
    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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  8.  99
    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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  9.  82
    Handbook of Philosophical Logic.Dov M. Gabbay & Franz Guenthner (eds.) - 1983 - Dordrecht, Netherland: 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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  10.  55
    A Logical Account of Formal Argumentation.Dov M. Gabbay - 2009 - 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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  11.  48
    A Logical Account of Formal Argumentation.Yining Wu, Martin Caminada & Dov M. Gabbay - 2009 - 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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  12. Handbook of Logic in Artificial Intelligence and Logic Programming.Dov M. Gabbay, Christopher John Hogger & J. A. Robinson - 1993
     
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  13. Handbook of the History of Logic.Dov M. Gabbay & John Woods - 2004 - Bulletin of Symbolic Logic 10 (4):579-583.
     
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  14. Agenda Relevance - a Study in Formal Pragmatics.Dov M. Gabbay & John Woods - 2003
     
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  15.  59
    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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  16.  9
    ‎Proof Theory for Fuzzy Logics.George Metcalfe, Nicola Olivetti & Dov M. Gabbay - 2008 - Dordrecht, Netherland: Springer.
    Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers (...)
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  17. Fibring Logics.Dov M. Gabbay - 2000 - Studia Logica 66 (3):440-443.
     
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  18.  16
    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.
  19.  3
    Adding a temporal dimension to a logic system.Dov M. Gabbay & Marcelo Finger - 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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  20.  28
    Fibring logics.Dov M. Gabbay - 1999 - New York: 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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  21.  94
    What is a logical system?Dov M. Gabbay (ed.) - 1994 - New York: 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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  22.  7
    On 2nd order intuitionistic propositional calculus with full comprehension.Dov M. Gabbay - 1974 - Archive for Mathematical Logic 16 (3-4):177-186.
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  23. What Is Negation?Dov M. Gabbay & Heinrich Wansing - 1999 - Studia Logica 69 (3):435-439.
  24.  32
    Expressive functional completeness in tense logic (preliminary report).Dov M. Gabbay - 1981 - In U. Mönnich (ed.), Aspects of Philosophical Logic. Dordrecht. pp. 91--117.
  25.  29
    Model theory for tense logics.Dov M. Gabbay - 1975 - Annals of Mathematical Logic 8 (1):185.
  26. 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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  27.  5
    Handbook of Tableau Methods.Marcello D'Agostino, Dov M. Gabbay, Reiner Hähnle & Joachim Posegga (eds.) - 1999 - Dordrecht, Netherland: Springer.
    Recent years have been blessed with an abundance of logical systems, arising from a multitude of applications. A logic can be characterised in many different ways. Traditionally, a logic is presented via the following three components: 1. an intuitive non-formal motivation, perhaps tie it in to some application area 2. a semantical interpretation 3. a proof theoretical formulation. There are several types of proof theoretical methodologies, Hilbert style, Gentzen style, goal directed style, labelled deductive system style, and so on. The (...)
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  28.  78
    A general theory of the conditional in terms of a ternary operator.Dov M. Gabbay - 1972 - Theoria 38 (3):97-104.
  29.  75
    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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  30. Agenda Relevance: A Study in Formal Pragmatics.Dov M. Gabbay & John Woods - 2004 - Studia Logica 77 (1):133-139.
     
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  31.  29
    Applications of trees to intermediate logics.Dov M. Gabbay - 1972 - Journal of Symbolic Logic 37 (1):135-138.
  32.  17
    The decidability of the Kreisel-Putnam system.Dov M. Gabbay - 1970 - Journal of Symbolic Logic 35 (3):431-437.
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  33. What Is a Logical System?Dov M. Gabbay - 1998 - Studia Logica 61 (2):302-304.
     
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  34. Handbook of Logic in Computer Science.Samson Abramsky, Dov M. Gabbay & Thomas S. E. Maibaum - 1992
     
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  35.  52
    Handbook of the logic of argument and inference: the turn towards the practical.Dov M. Gabbay (ed.) - 2002 - New York: 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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  36.  57
    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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  37.  42
    Semantics for Higher Level Attacks in Extended Argumentation Frames Part 1: Overview.Dov M. Gabbay - 2009 - 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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  38.  25
    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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  39. 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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  40.  40
    Montague Type Semantics for Modal Logics with Propositional Quantifiers.Dov M. Gabbay - 1971 - Mathematical Logic Quarterly 17 (1):245-249.
  41.  2
    What is Negation?Dov M. Gabbay & Heinrich Wansing (eds.) - 1999 - Dordrecht, Netherland: Springer.
    The properties of negation, in combination with those of other logical operations and structural features of the deductibility relation, serve as gateways among logical systems. Negation therefore plays an important role in selecting logical systems for particular applications. This volume provides a thorough treatment of this concept, based on contributions written by authors from various branches of logic. The resulting 14 research papers address a variety of topics including negation in relevant logics; a defense of dialetheic theory of negation; stable (...)
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  42.  17
    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.
  43.  13
    Decidability results in non-classical logics.Dov M. Gabbay - 1975 - Annals of Mathematical Logic 8 (3):237-295.
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  44.  26
    On some new intuitionistic propositional connectives. I.Dov M. Gabbay - 1977 - Studia Logica 36 (1-2):127 - 139.
  45.  55
    Philosophy of economics.Uskali Mäki, Dov M. Gabbay, Paul Thagard & John Woods (eds.) - 2012 - AMSTERDAM: 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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  46.  53
    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.
  47.  62
    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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  48.  33
    Sufficient conditions for the undecidability of intuitionistic theories with applications.Dov M. Gabbay - 1972 - Journal of Symbolic Logic 37 (2):375-384.
  49.  40
    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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  50.  30
    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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1 — 50 / 134