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  1. D. M. Gabbay (forthcoming). A Tense Logic with Split Truth Table. Logique Et Analyse.
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  2. M. Abraham, D. M. Gabbay & U. Schild (2012). Contrary to Time Conditionals in Talmudic Logic. Artificial Intelligence and Law 20 (2):145-179.
    We consider conditionals of the form A ⇒ B where A depends on the future and B on the present and past. We examine models for such conditional arising in Talmudic legal cases. We call such conditionals contrary to time conditionals.Three main aspects will be investigated: Inverse causality from future to past, where a future condition can influence a legal event in the past (this is a man made causality).Comparison with similar features in modern law.New types of temporal logics arising (...)
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  3. 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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  4. 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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  5. 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. D. M. Gabbay & U. Reyle (2012). Computation with Run Time Skolemisation (N-Prolog Part 3). Journal of Applied Non-Classical Logics 3 (1):93-128.
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  7. 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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  8. D. M. Gabbay (2011). Reactive Intuitionistic Tableaux. Synthese 179 (2):253 - 269.
    We introduce reactive Kripke models for intuitionistic logic and show that the reactive semantics is stronger than the ordinary semantics. We develop Beth tableaux for the reactive semantics.
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  9. D. M. Gabbay, F. Guenthner & Theo Mv Janssen (2007). REVIEWS-Handbook of Philosophical Logic, Vol. 10. Bulletin of Symbolic Logic 13 (2).
     
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  10. D. M. Gabbay, A. Kurucz, F. Wolter, M. Zakharyaschev & Mark Reynolds (2005). REVIEWS-Many-Dimensional Modal Logics: Theory and Applications. Bulletin of Symbolic Logic 11 (1):77-78.
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  11. D. M. Gabbay, G. Metcalfe & N. Olivetti (2005). Proof Theory for Propositional Fuzzy Logic. Logic Journal of the Igpl 13:561-585.
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  12. D. M. Gabbay, J. Woods & Klaus Glashoff (2004). REVIEWS-Handbook of the History of Logic. Volume 1: Greek, Indian and Arabian Logic. Bulletin of Symbolic Logic 10 (4):579-582.
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  13. Jon Williamson & D. M. Gabbay, Special Issue on Combining Probability and Logic.
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  14. P. Blackburn, A. Bochman, T. Clausing, P. Dekker, J. Engelfriet, D. M. Gabbay, F. Giunchiglia, J. M. Goñimenoyo, G. Jäger & T. M. V. Janssen (2002). Index of Authors of Volume 11. Journal of Logic, Language and Information 11 (519):519.
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  15. 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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  16. D. M. Gabbay (2002). A Theory of Hypermodal Logics: Mode Shifting in Modal Logic. [REVIEW] Journal of Philosophical Logic 31 (3):211-243.
    A hypermodality is a connective □ whose meaning depends on where in the formula it occurs. The paper motivates the notion and shows that hypermodal logics are much more expressive than traditional modal logics. In fact we show that logics with very simple K hypermodalities are not complete for any neighbourhood frames.
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  17. D. M. Gabbay & F. Guenthner (eds.) (2002). Handbook of Philosophical Logic, 2nd Edition. Kluwer.
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  18. 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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  19. D. M. Gabbay & U. Reyle (1997). Labelled Resolution for Classical and Non-Classical Logics. Studia Logica 59 (2):179-216.
    Resolution is an effective deduction procedure for classical logic. There is no similar "resolution" system for non-classical logics (though there are various automated deduction systems). The paper presents resolution systems for intuistionistic predicate logic as well as for modal and temporal logics within the framework of labelled deductive systems. Whereas in classical predicate logic resolution is applied to literals, in our system resolution is applied to L(abelled) R(epresentation) S(tructures). Proofs are discovered by a refutation procedure defined on LRSs, that imposes (...)
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  20. D. M. Gabbay (1996). Fibred Semantics and the Weaving of Logics Part 1: Modal and Intuitionistic Logics. Journal of Symbolic Logic 61 (4):1057-1120.
    This is Part 1 of a paper on fibred semantics and combination of logics. It aims to present a methodology for combining arbitrary logical systems L i , i ∈ I, to form a new system L I . The methodology `fibres' the semantics K i of L i into a semantics for L I , and `weaves' the proof theory (axiomatics) of L i into a proof system of L I . There are various ways of doing this, we (...)
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  21. D. M. Gabbay & V. B. Shehtman (1993). Undecidability of Modal and Intermediate First-Order Logics with Two Individual Variables. Journal of Symbolic Logic 58 (3):800-823.
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  22. D. M. Gabbay & Rjgb de Queiroz (1992). Extending the Curry {Howard {Tait Interpretation to Linear, Relevant and Other Logics. Journal of Symbolic Logic 56:1129-40.
     
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  23. 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.
  24. 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.
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  25. D. M. Gabbay & J. M. E. Moravcsik (1974). Branching Quantifiers, English and Montague Grammar. Theoretical Linguistics 1:140--157.
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  26. Jon Williamson & D. M. Gabbay, Recursive Causality in Bayesian Networks and Self-Fibring Networks.
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