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Profile: Dov Gabbay
  1.  24
    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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  2. Dov M. Gabbay, Ian Hodkinson & Mark Reynolds (1994). Temporal Logic Mathematical Foundations and Computational Aspects. Monograph Collection (Matt - Pseudo).
     
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  3.  47
    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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  4.  1
    Dov M. Gabbay (1986). Semantical Investigations in Heyting's Intuitionistic Logic. Journal of Symbolic Logic 51 (3):824-824.
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  5.  18
    D. M. Gabbay (2012). Equational Approach to Argumentation Networks. Argument and Computation 3 (2-3):87 - 142.
    This paper provides equational semantics for Dung's argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the ?extensions? of the network. This approach is very general and includes the Caminada labelling as a special case, as well as many other so-called network extensions, support systems, higher level attacks, Boolean networks, dependence on time, and much more. The equational approach has its conceptual roots in the nineteenth (...)
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  6.  78
    Dov M. Gabbay & Karl Schlechta (2009). Roadmap for Preferential Logics. Journal of Applied Non-Classical Logics 19 (1):43-95.
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  7.  23
    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 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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  8.  26
    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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  9.  44
    Dov M. Gabbay (1981). An Irreflexivity Lemma with Applications to Axiomatizations of Conditions on Tense Frames. In U. Mönnich (ed.), Aspects of Philosophical Logic. Dordrecht 67--89.
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  10.  22
    M. Abraham, D. M. Gabbay & U. Schild (2011). Obligations and Prohibitions in Talmudic Deontic Logic. Artificial Intelligence and Law 19 (2-3):117-148.
    This paper examines the deontic logic of the Talmud. We shall find, by looking at examples, that at first approximation we need deontic logic with several connectives: O T A Talmudic obligation F T A Talmudic prohibition F D A Standard deontic prohibition O D A Standard deontic obligation. In classical logic one would have expected that deontic obligation O D is definable by $O_DA \equiv F_D\neg A$ and that O T and F T are connected by $O_TA \equiv F_T\neg (...)
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  11.  30
    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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  12.  29
    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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  13.  8
    S. Chopra, B. J. Copeland, E. Corazza, S. Donaho, F. Ferreira, H. Field, D. M. Gabbay, L. Goldstein, J. Heidema & M. J. Hill (2002). Benton, RA, 527 Blackburn, P., 281 Braüner, T., 359 Brink, C., 543. Journal of Philosophical Logic 31 (615).
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  14.  19
    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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  15.  37
    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.  13
    Dov M. Gabbay & Artur S. D'Avila Garcez (2009). Logical Modes of Attack in Argumentation Networks. 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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  17.  1
    D. Gabbay & V. Shehtman (1998). Products of Modal Logics, Part 1. Logic Journal of the IGPL 6 (1):73-146.
    The paper studies many-dimensional modal logics corresponding to products of Kripke frames. It proves results on axiomatisability, the finite model property and decidability for product logics, by applying a rather elaborated modal logic technique: p-morphisms, the finite depth method, normal forms, filtrations. Applications to first order predicate logics are considered too. The introduction and the conclusion contain a discussion of many related results and open problems in the area.
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  18.  6
    H. Barringer, D. M. Gabbay & J. Woods (2012). Temporal, Numerical and Meta-Level Dynamics in Argumentation Networks. Argument and Computation 3 (2-3):143 - 202.
    This paper studies general numerical networks with support and attack. Our starting point is argumentation networks with the Caminada labelling of three values 1=in, 0=out and ½=undecided. This is generalised to arbitrary values in [01], which enables us to compare with other numerical networks such as predator?prey ecological networks, flow networks, logical modal networks and more. This new point of view allows us to see the place of argumentation networks in the overall landscape of networks and import and export ideas (...)
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  19.  25
    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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  20.  20
    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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  21. 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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  22. G. Boella, D. M. Gabbay, L. van der Torre & S. Villata (2009). Argumentation Modelling of the Toulmin Scheme. Studia Logica 93 (2-3):297-354.
     
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  23.  38
    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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  24.  35
    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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  25.  15
    Dov M. Gabbay & Artur S. D’Avila Garcez (2009). Logical Modes of Attack in Argumentation Networks. 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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  26.  16
    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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  27.  4
    Guido Boella, Dov M. Gabbay, Valerio Genovese & Leendert Van Der Torre (2009). Fibred Security Language. 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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  28.  1
    J. Bicarregui, T. Dimitrakos, D. Gabbay & T. Maibaum (2001). Interpolation in Practical Formal Development. Logic Journal of the IGPL 9 (2):231-244.
    Interpolation has become one of the standard properties that logicians investigate when designing a logic. In this paper, we provide strong evidence that the presence of interpolants is not only cogent for scientific reasoning but has also important practical implications in computer science. We illustrate that interpolation in general, and uniform splitting interpolants, in particular, play an important role in applications where formality and modularity are invoked. In recognition of the fact that common logical formalisms often lack uniform interpolants, we (...)
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  29.  23
    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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  30.  11
    H. Barringer, D. M. Gabbay & J. Woods (2012). Modal and Temporal Argumentation Networks. Argument and Computation 3 (2-3):203 - 227.
    The traditional Dung networks depict arguments as atomic and study the relationships of attack between them. This can be generalised in two ways. One is to consider various forms of attack, support, feedback, etc. Another is to add content to nodes and put there not just atomic arguments but more structure, e.g. proofs in some logic or simply just formulas from a richer language. This paper offers to use temporal and modal language formulas to represent arguments in the nodes of (...)
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  31. D. M. Gabbay & D. H. J. de Jongh (1974). A Sequence of Decidable Finitely Axiomatizable Intermediate Logics with the Disjunction Property. Journal of Symbolic Logic 39 (1):67-78.
  32.  6
    Dov M. Gabbay (2000). Goal-Directed Proof Theory. 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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  33.  43
    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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  34.  36
    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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  35.  35
    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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  36.  20
    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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  37. Dov M. Gabbay & Heinrich Wansing (2001). What Is Negation? Studia Logica 69 (3):435-439.
     
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  38.  13
    Marcelo Finger & Dov Gabbay (2006). Cut and Pay. Journal of Logic, Language and Information 15 (3):195-218.
    In this paper we study families of resource aware logics that explore resource restriction on rules; in particular, we study the use of controlled cut-rule and introduce three families of parameterised logics that arise from different ways of controlling the use of cut. We start with a formulation of classical logic in which cut is non-eliminable and then impose restrictions on the use of cut. Three Cut-and-Pay families of logics are presented, and it is shown that each family provides an (...)
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  39.  70
    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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  40. Samson Abramsky, Dov M. Gabbay & Thomas S. E. Maibaum (1992). Handbook of Logic in Computer Science. Monograph Collection (Matt - Pseudo).
     
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  41.  10
    Dov M. Gabbay (1999). Fibring Logics. 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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  42.  26
    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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  43. Dov M. Gabbay (1979). Investigations in Modal and Tense Logics with Application to Problems in Philosophy and Linguistics. Journal of Symbolic Logic 44 (4):656-657.
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  44. D. Gabbay & F. Pirri (forthcoming). Special Issue on Combining Logics, Volume 59 (1, 2) Of. Studia Logica.
     
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  45.  14
    Guido Boella, Dov M. Gabbay, Valerio Genovese & Leendert van der Torre (2009). Fibred Security Language. 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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  46.  5
    Dov M. Gabbay & Karl Schlechta (2010). Semantic Interpolation. Journal of Applied Non-Classical Logics 20 (4):345-371.
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  47.  33
    Mathijs Boer, Dov M. Gabbay, Xavier Parent & Marija Slavkovic (2012). Two Dimensional Standard Deontic Logic [Including a Detailed Analysis of the 1985 Jones–Pörn Deontic Logic System]. 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.  33
    D. M. Gabbay & G. Malod (2002). Naming Worlds in Modal and Temporal Logic. Journal of Logic, Language and Information 11 (1):29-65.
    In this paper we suggest adding to predicate modal and temporal logic a locality predicate W which gives names to worlds (or time points). We also study an equal time predicate D(x, y)which states that two time points are at the same distance from the root. We provide the systems studied with complete axiomatizations and illustrate the expressive power gained for modal logic by simulating other logics. The completeness proofs rely on the fairly intuitive notion of a configuration in order (...)
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  49.  14
    Mathijs de Boer, Dov M. Gabbay, Xavier Parent & Marija Slavkovic (2012). Two Dimensional Standard Deontic Logic [Including a Detailed Analysis of the 1985 Jones–Pörn Deontic Logic System]. 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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  50. D. M. Gabbay & F. Guenthner (eds.) (2011). Handbook of Philosophical Logic Vol. 15. Kluwer Academic Publishers.
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