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  1. Dov M. Gabbay & John Woods, Advice on Abductive Logic.
    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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  2. Dov Gabbay, Stephan Hartmann & John Woods (eds.) (forthcoming). Handbook of the History and Philosophy of Logic, Vol. 10: Inductive Logic. Elsevier.
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  3. Dov Gabbay, Stephan Hartmann & John Woods (eds.) (forthcoming). Handbook of the History of Logic, Vol. 10. Elsevier.
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  4. Alexander Bochman & Dov M. Gabbay (2012). Sequential Dynamic Logic. Journal of Logic, Language and Information 21 (3):279-298.
    We introduce a substructural propositional calculus of Sequential Dynamic Logic that subsumes a propositional part of dynamic predicate logic, and is shown to be expressively equivalent to propositional dynamic logic. Completeness of the calculus with respect to the intended relational semantics is established.
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  5. 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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  6. 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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  7. 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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  8. Michael Abraham, Dov M. Gabbay, Gabriel Hazut, Yosef E. Maruvka & Uri Schild (2011). Logical Analysis of the Talmudic Rules of General and Specific (Klalim-U-Pratim). History and Philosophy of Logic 32 (1):47-62.
    This article deals with a set-theoretic interpretation of the Talmudic rules of General and Specific, known as Klal and Prat (KP), Prat and Klal (PK), Klal and Prat and Klal (KPK) and Prat and Klal and Prat (PKP).
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  9. Dov M. Gabbay (2011). Dung's Argumentation is Essentially Equivalent to Classical Propositional Logic with the Peirce–Quine Dagger. 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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  10. Dov M. Gabbay & Moshe Koppel (2011). Uncertainty Rules in Talmudic Reasoning. History and Philosophy of Logic 32 (1):63-69.
    The Babylonian Talmud, compiled from the 2nd to 7th centuries C.E., is the primary source for all subsequent Jewish laws. It is not written in apodeictic style, but rather as a discursive record of (real or imagined) legal (and other) arguments crossing a wide range of technical topics. Thus, it is not a simple matter to infer general methodological principles underlying the Talmudic approach to legal reasoning. Nevertheless, in this article, we propose a general principle that we believe helps to (...)
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  11. Dov M. Gabbay & Karl Schlechta (2010). A Comment on Work by Booth and Co-Authors. Studia Logica 94 (3):403 - 432.
    Booth and his co-authors have shown in [2], that many new approaches to theory revision (with fixed K ) can be represented by two relations, , where is a sub-relation of < . They have, however, left open a characterization of the infinite case, which we treat here.
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  12. Dov M. Gabbay & Karl Schlechta (2010). A Theory of Hierarchical Consequence and Conditionals. Journal of Logic, Language and Information 19 (1):3-32.
    We introduce -ranked preferential structures and combine them with an accessibility relation. -ranked preferential structures are intermediate between simple preferential structures and ranked structures. The additional accessibility relation allows us to consider only parts of the overall -ranked structure. This framework allows us to formalize contrary to duty obligations, and other pictures where we have a hierarchy of situations, and maybe not all are accessible to all possible worlds. Representation results are proved.
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  13. Dov M. Gabbay & Karl Schlechta (2010). Semantic Interpolation. Journal of Applied Non-Classical Logics 20 (4):345-371.
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  14. M. Abraham, Dov M. Gabbay & U. Schild (2009). Analysis of the Talmudic Argumentum a Fortiori Inference Rule (Kal Vachomer) Using Matrix Abduction. 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 (...)
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  15. Steve Barker, Guido Boella, Dov M. Gabbay & Valerio Genovese (2009). A Meta-Model of Access Control in a Fibred Security Language. Studia Logica 92 (3):437 - 477.
    The issue of representing access control requirements continues to demand significant attention. The focus of researchers has traditionally been on developing particular access control models and policy specification languages for particular applications. However, this approach has resulted in an unnecessary surfeit of models and languages. In contrast, we describe a general access control model and a logic-based specification language from which both existing and novel access control models may be derived as particular cases and from which several approaches can be (...)
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  16. 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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  17. 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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  18. Guido Boella, Dov M. Gabbay, Leendert van der Torre & Serena Villata (2009). Meta-Argumentation Modelling I: Methodology and Techniques. 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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  19. Guido Boella, Dov M. Gabbay, Leendert van der Torre & Serena Villata (2009). Meta-Argumentation Modelling I: Methodology and Techniques. [REVIEW] Studia Logica 93 (2-3):297-355.
    In this paper, we introduce the methodology and techniques of meta-argumentation 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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  20. 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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  21. Dov Gabbay (ed.) (2009). The Handbook of the History of Logic. Elsevier.
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  22. 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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  23. 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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  24. 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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  25. Dov M. Gabbay & Artur S. D'Avila Garcez (2009). Logical Modes of Attack in Argumentation Networks. Studia Logica 93 (2-3):199-230.
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  26. 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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  27. 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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  28. Dov M. Gabbay & Karl Schlechta (2009). Independence — Revision and Defaults. Studia Logica 92 (3):381 - 394.
    We investigate different aspects of independence here, in the context of theory revision, generalizing slightly work by Chopra, Parikh, and Rodrigues, and in the context of preferential reasoning.
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  29. Dov M. Gabbay & Karl Schlechta (2009). Roadmap for Preferential Logics. Journal of Applied Non-Classical Logics 19 (1):43-95.
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  30. 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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  31. 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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  32. Dov M. Gabbay & Andrzej Szałas (2009). Annotation Theories Over Finite Graphs. Studia Logica 93 (2/3):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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  33. Dov M. Gabbay & Andrzej Szałas (2009). Voting by Eliminating Quantifiers. Studia Logica 92 (3):365 - 379.
    Mathematical theory of voting and social choice has attracted much attention. In the general setting one can view social choice as a method of aggregating individual, often conflicting preferences and making a choice that is the best compromise. How preferences are expressed and what is the “best compromise” varies and heavily depends on a particular situation. The method we propose in this paper depends on expressing individual preferences of voters and specifying properties of the resulting ranking by means of first-order (...)
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  34. Dov M. Gabbay & Leendert van der Torre (2009). Preface for Studia Logica Special Issue (2). Studia Logica 93 (2/3):105 - 108.
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  35. Dov M. Gabbay & Leendert van der Torre (2009). Preface for Studia Logica Special Issue (2). Studia Logica 93 (2-3):105-108.
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  36. Dov M. Gabbay & John Woods (2009). Fallacies as Cognitive Virtues. In. In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy. Springer Verlag. 57--98.
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  37. Thierry Libert, T. Forster, R. Holmes, Dov M. Gabbay, John Woods & Akihiro Kanamori (2009). Alternative Set Theories. In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier.
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  38. 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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  39. Dov M. Gabbay & Karl Schlechta (2008). Cumulativity Without Closure of the Domain Under Finite Unions. Review of Symbolic Logic 1 (3):372-392.
    For nonmonotonic logics, Cumulativity is an important logical rule. We show here that Cumulativity fans out into an infinity of different conditions, if the domain is not closed under finite unions.
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  40. 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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  41. 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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  42. Ruth Kempson, Marcelo Finger, Rodger Kibble & Dov Gabbay, Parsing Natural Language Using LDS: A Prototype.
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  43. Ruth Kempson, Wilfried Meyer-Viol, Rodger Dibble & Dov Gabbay, Indefinites as Epsilon Terms: A Labelled Deduction Account.
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  44. Ruth Kempson, Wilfried Meyer-Viol & Dov Gabbay, Language Understanding: A Procedural Perspective.
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  45. Ruth Kempson, Wilfried Meyer-Viol & Dov Gabbay, Syntactic Computation as Labelled Deduction: WH a Case Study.
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  46. H. Cowles, Matthew Walenski, Robert Kluender, Markus Knauff, Artur S. Davila Garcez, Dov M. Gabbay, Oliver Ray, John Woods, Robin Clark & Murray Grossman (2007). Logic and Cognition. Topoi 26 (1).
     
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  47. 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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  48. 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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  49. 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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