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Reactive Preferential Structures and Nonmonotonic consequence Gabbay, Dov M. ; in Review of Symbolic Logic (The) (2009), 2(2), 414450 We introduce Information Bearing Relation Systems (IBRS) a s an abstraction of many logical systems. We then define a general semantics for IBRS, and show that a special case of IBRS generalizes in a very ... [more ▼] We introduce Information Bearing Relation Systems (IBRS) a s an abstraction of many logical systems. 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 ”break” the strong coher ence properties of preferential structures by higher arrows, i.e. arrows, which do not go to points, but t o arrows themselves [less ▲] Detailed reference viewed: 24 (0 UL)Semantics for Higher Level Attacks in Extended Argumentation Frames Part 1: Overview Gabbay, Dov M. in Studia Logica (2009), 93(2-3), 357381 In 2005 the author introduced networks which allow attacks on attacks of any level. So if a→b reads a attacks b, then this attack can itself be attacked by another node c. This attack itself can attack ... [more ▼] In 2005 the author introduced networks which allow attacks on attacks of any level. So if a→b reads a attacks b, 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. [less ▲] Detailed reference viewed: 33 (3 UL)Meta-Argumentation part 1 Boella, Guido ; Gabbay, Dov M. ; van der Torre, Leon et al in Studia Logica (2009) 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 ... [more ▼] 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. We characterize the domain of instantiation using a representation technique based on soundness and completeness. Finally, we distinguish among various instantiations using the technique of specification languages. [less ▲] Detailed reference viewed: 24 (0 UL)Fibring Argumentation Frames Gabbay, Dov M. in Studia Logica (2009) 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 ... [more ▼] 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 how to bring logic and networks closer together. Section 3 develops the formal properties of the new kind of network and Section 4 offers general discussion and comparison with the literature. [less ▲] Detailed reference viewed: 20 (1 UL)Reactive Kripke Models and Contrary to Duty Obligations Gabbay, Dov M. in Deontic Logic in Computer Science, 9th International Conference, DEON 2008, Luxembourg, Luxembourg, July 15-18, 2008. Proceedings (2008) This is an intuitive description of our approach to modelling contrary to duty obliga- tions. We shall describe our ideas through the analysis of typical problematic examples taken from Carmo and Jones [6 ... [more ▼] This is an intuitive description of our approach to modelling contrary to duty obliga- tions. We shall describe our ideas through the analysis of typical problematic examples taken from Carmo and Jones [6], L. van der Torre [14] and Prakken and Sergot [5] [less ▲] Detailed reference viewed: 17 (1 UL)A Sound and Complete Deductive System for CTL Verification Gabbay, Dov M. ; in Journal of Logic & Computation (2008), 16(6), 499536 Detailed reference viewed: 25 (0 UL)Quantum Logic Gabbay, Dov M. ; ; Book published by College publications (2008) Detailed reference viewed: 4 (0 UL)Belief Revision in Non-classical Logic II Gabbay, Dov M. ; ; in Review of Symbolic Logic (The) (2008), 1(03), 267304 Detailed reference viewed: 20 (1 UL)Connectionist Non-classical Logics: Distributed Reasoning & Learning in Neural Networks Gabbay, Dov M. ; Garcez, A. S. D. Avila ; Lamb, L. C. Book published by Springer-Verlag (2008) Detailed reference viewed: 17 (0 UL)Analysis and synthesis of logics ; ; Gabbay, Dov M. et al Book published by Springer (2008) Detailed reference viewed: 16 (0 UL)Belief Revision Gabbay, Dov M. ; ; in Handbook of Philosophical Logic (2008) Detailed reference viewed: 11 (1 UL)Cut-Based Abduction ; Gabbay, Dov M. in Journal of Logic & Computation (2008), 16(6), 537560 In this paper we explore a generalization of traditional abduction which can simultaneously perform two different tasks: (i) given an unprovable sequent G, find a sentence H such that, H G is provable ... [more ▼] In this paper we explore a generalization of traditional abduction which can simultaneously perform two different tasks: (i) given an unprovable sequent G, find a sentence H such that, H G is provable (hypothesis generation); (ii) given a provable sequent G, find a sentence H such that H and the proof of , H G is simpler than the proof of G (lemma generation). We argue that the two tasks should not be distinguished,and present a general procedure for indingsuitable hypotheses or lemmas. When the original sequent is provable, the abduced formula can be seen asa cut formula with respect to Gentzen's sequent calculus, so the abduction method is cut-based. Our method is based on the tableau-like system KE and we argue for its advantages over existing abduction methods based on traditional Smullyan-styleTableaux. [less ▲] Detailed reference viewed: 18 (0 UL)Introducing Reactive Kripke Semantics and Arc Accessibility Gabbay, Dov M. in Pillars of Computer Science, Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday (2008) Ordinary Kripke models are not reactive. When we evaluate (test/ measure) a formula A at a model m, the model does not react, respond or change while we evaluate. The model is static and unchanged. This ... [more ▼] Ordinary Kripke models are not reactive. When we evaluate (test/ measure) a formula A at a model m, the model does not react, respond or change while we evaluate. The model is static and unchanged. This paper studies Kripke models which react to the evaluation process and change themselves during the process. The additional device we add to Kripke semantics to make it reactive is to allow the accessibility relation to access itself. Thus the accessibility relation R of a reactive Kripke model contains not only pairs (a,b)∈R of possible worlds (b is accessible to a, i.e., there is an accessibility arc from a to b) but also pairs of the form (t,(a,b))∈R, meaning that the arc (a,b) is accessible to t, or even connections of the form ((a,b), (c,d))∈R. This new kind of Kripke semantics allows us to characterise more axiomatic odal logics (with one modality []) by a class of reactive frames. There are logics which cannot be characterised by ordinary frames but which can be characterised by reactive frames. We also discuss the manifestation of the ‘reactive’ idea in the context of automata theory, where we allow the automaton to react and change it’s own definition as it responds to input, and in graph theory, where the graph can change under us as we manipulate it. [less ▲] Detailed reference viewed: 21 (0 UL)A Normative View on The Blocks World Grossi, Davide ; Gabbay, Dov M. ; van der Torre, Leon in Proceedings of the 3rd International Workshop on Normative Multiagent Systems (NorMAS'08) (2008) Detailed reference viewed: 32 (1 UL)Resource-origins of Nonmonotonicity Gabbay, Dov M. ; in Studia Logica (2008), 88(1), 85112 Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning from assumptions ∆ to conclusions C without their being any deductive chain from ∆ ... [more ▼] Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning from assumptions ∆ to conclusions C without their being any deductive chain from ∆ 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. We begin with a general discussion and quickly move to Section 3 where we introduce five resource principles. We show that these principles lead to some well known nonmonotonic systems such as Nute’s defeasible logic. We also give several examples of practical reasoning situations to illustrate our principles. [less ▲] Detailed reference viewed: 20 (0 UL)Cumulativity without closure of the domain under finite unions Gabbay, Dov M. ; in Review of Symbolic Logic (The) (2008), 1(03), 267304 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. Detailed reference viewed: 17 (0 UL)Second-order Quantifier Elimination Foundations, Computational Aspects and Applications (Studies in Logic Mathematical Logic and Foundations) Gabbay, Dov M. ; ; Book published by College publications (2008) Detailed reference viewed: 63 (0 UL)A New Approach to Quantum Logic ; Gabbay, Dov M. ; Book published by College publications (2007) Detailed reference viewed: 30 (0 UL)Common Foundations for Belief Revision, Belief Merging and Voting Gabbay, Dov M. ; Pigozzi, Gabriella ; in Formal Models of Belief Change in Rational Agents (2007) In this paper, we consider a number of different ways of reasoning about voting as a problem of conciliating contradictory interests. The mechanisms that do the reconciliation are belief revision and be ... [more ▼] In this paper, we consider a number of different ways of reasoning about voting as a problem of conciliating contradictory interests. The mechanisms that do the reconciliation are belief revision and be- lief merging. By investigating the relationship between different voting strategies and their associated counterparts in revision theory, we find that whereas the counting mechanism of the voting process is more easily done at the meta-level in belief merging, it can be brought to the object level in base revision. In the former case, the counting can b e tweaked according to the aggregation procedure used, whereas in base revision, we can only rely on the notion of minimal change and hence the syntactical representation of the voters’ preferences plays a crucial part in the process. This highlights the similarities between the revi sion approaches on the one hand and voting on the other, but also opens up a numb er of interesting questions. [less ▲] Detailed reference viewed: 8 (0 UL)Belief revision, belief merging and voting Gabbay, Dov M. ; Pigozzi, Gabriella ; in Proceedings of the Seventh Conference on Logic and the Foundations of Games and Decision Theory (LOFT06) (2006) In belief revision, an agent is faced with the problem of choosing between several alternatives when trying to restore con- sistency to theory. Ideally, the choice process is conducted in a way that ... [more ▼] In belief revision, an agent is faced with the problem of choosing between several alternatives when trying to restore con- sistency to theory. Ideally, the choice process is conducted in a way that verifies a number of fairness principles. On the other hand, be- lief merging concerns with the problem of determining a group’s be- liefs from individual members’ beliefs that are not always compatible with each other. Similarly, in voting systems, a social welfare func- tion takes individual preferences into account in order to produce a collective preference. Here again certain fairness principles are desir- able. In this paper, we investigate the relationship between revision, merging and voting. [less ▲] Detailed reference viewed: 9 (0 UL) |
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