121 found
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  1.  74
    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.  93
    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.  47
    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.  40
    Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1986 - Journal of Symbolic Logic 51 (3):824-824.
  5.  13
    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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  6.  86
    An irreflexivity lemma with applications to axiomatizations of conditions on tense frames.Dov M. Gabbay - 1981 - In Uwe Mönnich (ed.), Aspects of Philosophical Logic: Some Logical Forays Into Central Notions of Linguistics and Philosophy. Dordrecht, Netherland: Dordrecht. pp. 67--89.
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  7. 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. (1 other version)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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  9.  46
    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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  10.  49
    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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  11. Handbook of Logic in Artificial Intelligence and Logic Programming.Dov M. Gabbay, Christopher John Hogger & J. A. Robinson - 1993
     
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  12. Handbook of the History of Logic.Dov M. Gabbay & John Woods - 2004 - Bulletin of Symbolic Logic 10 (4):579-583.
     
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  13.  65
    Logical Modes of Attack in Argumentation Networks.Dov M. Gabbay & Artur S. D’Avila Garcez - 2009 - Studia Logica 93 (2):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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  14. Agenda Relevance - a Study in Formal Pragmatics.Dov M. Gabbay & John Woods - 2003
     
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  15.  24
    ‎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 (...)
  16. Fibring Logics.Dov M. Gabbay - 2000 - Studia Logica 66 (3):440-443.
     
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  17.  23
    (1 other version)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.
  18.  16
    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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  19.  35
    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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  20. 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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  21. What Is Negation?Dov M. Gabbay & Heinrich Wansing - 1999 - Studia Logica 69 (3):435-439.
  22.  40
    Expressive functional completeness in tense logic (preliminary report).Dov M. Gabbay - 1981 - In Uwe Mönnich (ed.), Aspects of Philosophical Logic: Some Logical Forays Into Central Notions of Linguistics and Philosophy. Dordrecht, Netherland: Dordrecht. pp. 91--117.
  23.  30
    Model theory for tense logics.Dov M. Gabbay - 1975 - Annals of Mathematical Logic 8 (1):185.
  24.  41
    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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  25.  70
    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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  26.  97
    A general theory of the conditional in terms of a ternary operator.Dov M. Gabbay - 1972 - Theoria 38 (3):97-104.
  27. What Is a Logical System?Dov M. Gabbay - 1998 - Studia Logica 61 (2):302-304.
     
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  28.  57
    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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  29.  14
    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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  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.  60
    Applications of trees to intermediate logics.Dov M. Gabbay - 1972 - Journal of Symbolic Logic 37 (1):135-138.
  32.  34
    The decidability of the Kreisel-Putnam system.Dov M. Gabbay - 1970 - Journal of Symbolic Logic 35 (3):431-437.
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  33. Handbook of Logic in Computer Science.Samson Abramsky, Dov M. Gabbay & Thomas S. E. Maibaum - 1992
     
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  34. 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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  35.  56
    Analysis of the Talmudic Argumentum A Fortiori Inference Rule (Kal Vachomer) 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 $${\mathbb {A}}$$ 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 =? (...)
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  36.  43
    Montague Type Semantics for Modal Logics with Propositional Quantifiers.Dov M. Gabbay - 1971 - Mathematical Logic Quarterly 17 (1):245-249.
  37.  39
    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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  38.  34
    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. Dordrecht, Netherland: Springer Verlag. pp. 57--98.
  39.  17
    A practical logic of cognitive systems.Dov M. Gabbay - 2003 - Boston: North Holland. Edited by John Woods.
    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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  40.  20
    Decidability results in non-classical logics.Dov M. Gabbay - 1975 - Annals of Mathematical Logic 8 (3):237-295.
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  41.  48
    On some new intuitionistic propositional connectives. I.Dov M. Gabbay - 1977 - Studia Logica 36 (1-2):127 - 139.
  42.  64
    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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  43.  76
    (1 other version)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.
  44.  67
    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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  45.  94
    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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  46.  59
    Sufficient conditions for the undecidability of intuitionistic theories with applications.Dov M. Gabbay - 1972 - Journal of Symbolic Logic 37 (2):375-384.
  47.  42
    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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  48.  8
    Logical Tools for Handling Change in Agent-Based Systems.Dov M. Gabbay & Karl Schlechta - 2009 - New York, NY, USA: Springer.
    Agents act on the basis of their beliefs and these beliefs change as they interact with other agents. In this book the authors propose and explain general logical tools for handling change. These tools include preferential reasoning, theory revision, and reasoning in inheritance systems, and the authors use these tools to examine nonmonotonic logic, deontic logic, counterfactuals, modal logic, intuitionistic logic, and temporal logic. This book will be of benefit to researchers engaged with artificial intelligence, and in particular agents, multiagent (...)
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  49.  85
    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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  50.  18
    (1 other version)Model Theory for Intuitionistic Logic.Dov M. Gabbay - 1972 - Mathematical Logic Quarterly 18 (4‐6):49-54.
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