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A logical account of formal argumentation Caminada, Martin ; Gabbay, Dov M. in Studia Logica (2009) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 86 (2 UL)An Analysis of Defeasible Inheritance Systems Gabbay, Dov M. ; in Logic Journal of the IGPL (2009) Detailed reference viewed: 65 (0 UL)Logical Modes of Attack in Argumentation Networks Gabbay, Dov M. ; in Studia Logica (2009) 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 ... [more ▼] 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 meta level 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 systems. We also provide a number of examples and consider a rigorous case study, which indicate that our system does not suffer from anomalies. We define consequence relations based on a notion of defeat, consider rationality postulates, and prove that one such consequence relation is consistent. [less ▲] Detailed reference viewed: 59 (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: 75 (1 UL)Voting by Eliminating Quantifiers Gabbay, Dov M. ; in Studia Logica (2009), 92(3), 365379 Mathematical theory of voting and social choice has attracted much at- tention. In the general setting one can view social choice as a method of aggregating individual, often conflicting preferences and ... [more ▼] Mathematical theory of voting and social choice has attracted much at- tention. 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 formulas. Then, as a technical tool, we use methods of second-order quantifier elimination to analyze and compute results of voting. We show how to specify voting, how to compute resulting rankings and how to verify voting protocols. [less ▲] Detailed reference viewed: 72 (0 UL)Logical Tools for Handling Change in Agent-based Systems Gabbay, Dov M. ; Book published by Springer (2009) Detailed reference viewed: 50 (0 UL)Revision, Acceptability and Context Gabbay, Dov M. ; ; Book published by Springer (2009) Detailed reference viewed: 52 (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: 85 (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: 30 (1 UL)Analysis and synthesis of logics ; ; Gabbay, Dov M. et al Book published by Springer (2008) Detailed reference viewed: 59 (0 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: 23 (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: 40 (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: 73 (0 UL)Belief Revision Gabbay, Dov M. ; ; in Handbook of Philosophical Logic (2008) Detailed reference viewed: 11 (1 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: 74 (0 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: 58 (1 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: 62 (0 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: 26 (0 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: 71 (1 UL)Quantum Logic Gabbay, Dov M. ; ; Book published by College publications (2008) Detailed reference viewed: 8 (0 UL) |
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