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Global view on reactivity: switch graphs and their logics Gabbay, Dov M. ; in Annals of Mathematics & Artificial Intelligence (2012), 66(1-4), 131-162 The notion of reactive graph generalises the one of graph by allowing the base accessibility relation to change when its edges are traversed. Can we represent these more general structures using points ... [more ▼] The notion of reactive graph generalises the one of graph by allowing the base accessibility relation to change when its edges are traversed. Can we represent these more general structures using points and arrows? We prove this can be done by introducing higher order arrows: the switches. The possibility of expressing the dependency of the future states of the accessibility relation on individual transitions by the use of higher-order relations, that is, coding meta-relational concepts by means of relations, strongly suggests the use of modal languages to reason directly about these structures. We introduce a hybrid modal logic for this purpose and prove its completeness. [less ▲] Detailed reference viewed: 74 (5 UL)Introducing reactive Kripke semantics and arc accessibility Gabbay, Dov M. in Annals of Mathematics & Artificial Intelligence (2012), 66(1-4), 7-53 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 modal 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: 68 (4 UL)Introducing reactive modal tableaux Gabbay, Dov M. in Annals of Mathematics & Artificial Intelligence (2012), 66(1-4), 55-79 This paper introduces the idea of reactive semantics and reactive Beth tableaux for modal logic and quotes some of its applications. The reactive idea is very simple. Given a system with states and the ... [more ▼] This paper introduces the idea of reactive semantics and reactive Beth tableaux for modal logic and quotes some of its applications. The reactive idea is very simple. Given a system with states and the possibility of transitions moving from one state to another, we can naturally imagine a path beginning at an initial state and moving along the path following allowed transitions. If our starting point is s0, and the path is s0,s1,...,sn, then the system is ordinary non-reactive system if the options available at sn (i.e., which states t we can go to from sn) do not depend on the path s0,...,sn (i.e., do not depend on how we got to sn). Otherwise if there is such dependence then the system is reactive. It seems that the simple idea of taking existing systems and turning them reactive in certain ways, has many new applications. The purpose of this paper is to introduce reactive tableaux in particular and illustrate and present some of the applications of reactivity in general. Mathematically one can take a reactive system and turn it into an ordinary system by taking the paths as our new states. This is true but from the point of view of applications there is serious loss of information here as the applicability of the reactive system comes from the way the change occurs along the path. In any specific application, the states have meaning, the transitions have meaning and the paths have meaning. Therefore the changes in the system as we go along a path can have very important meaning in the context, which enhances the usability of the model. [less ▲] Detailed reference viewed: 72 (4 UL)Bipolar Argumentation Frames and Contrary to Duty Obligations, Preliminary Report Gabbay, Dov M. in Computational Logic in Multi-Agent Systems - 13th International Workshop CLIMA XIII, Montpellier, France, August 27-28, 2012. Proceedings (2012) Detailed reference viewed: 52 (0 UL)Logic: A History of its Central Concepts Gabbay, Dov M. ; ; Book published by Elsevier (2012) Detailed reference viewed: 92 (0 UL)A Numerical Approach to the Merging of Argumentation Networks Gabbay, Dov M. ; in Fisher, Michael; Torre, Leon; Dastani, Mehdi (Eds.) et al Computational Logic in Multi-Agent Systems (2012) In this paper, we propose a numerical approach to the problem of merging of argumentation networks. The idea is to consider an augmented network containing the arguments and attacks of all networks to be ... [more ▼] In this paper, we propose a numerical approach to the problem of merging of argumentation networks. The idea is to consider an augmented network containing the arguments and attacks of all networks to be merged and then associate a weight to each of its components based on how they are perceived by the agents associated with the local networks. The combined weighted network is then used to define a system of equations from which the overall strength of the arguments is calculated. [less ▲] Detailed reference viewed: 84 (0 UL)Contrary to time conditionals in Talmudic logic ; Gabbay, Dov M. ; in Artif. Intell. Law (2012), 20(2), 145--179 Detailed reference viewed: 60 (0 UL)Sets and Extensions in the Twentieth Century Gabbay, Dov M. ; ; Book published by Elsevier (2012) Detailed reference viewed: 66 (0 UL)Preface Gabbay, Dov M. ; ; in Logic: A History of its Central Concepts (2012) Detailed reference viewed: 8 (0 UL)An Equational Approach to Logic Programming Gabbay, Dov M. in Correct Reasoning - Essays on Logic-Based AI in Honour of Vladimir Lifschitz (2012) Detailed reference viewed: 43 (0 UL)Sequential Dynamic Logic ; Gabbay, Dov M. in Journal of Logic, Language and Information (2012), 21(3), 279--298 Detailed reference viewed: 58 (0 UL)What Is Negation as Failure? Gabbay, Dov M. in Logic Programs, Norms and Action - Essays in Honor of Marek J. Sergot on the Occasion of His 60th Birthday (2012) Detailed reference viewed: 79 (0 UL)The Equational Approach to CF2 Semantics Gabbay, Dov M. in Computational Models of Argument - Proceedings of COMMA 2012, Vienna Austria, September 10-12, 2012 (2012) Detailed reference viewed: 16 (0 UL)Discussion Paper: Changing Norms Is Changing Obligation Change Broersen, Jan ; Gabbay, Dov M. ; van der Torre, Leon in Deontic Logic in Computer Science (2012) Detailed reference viewed: 83 (5 UL)A logic of argumentation for specification and verification of abstract argumentation frameworks ; ; Gabbay, Dov M. et al in Annals of Mathematics & Artificial Intelligence (2012), 66(1-4), 199-230 In this paper, we propose a logic of argumentation for the specification and verification (LA4SV) of requirements on Dung’s abstract argumentation frameworks. We distinguish three kinds of decision ... [more ▼] In this paper, we propose a logic of argumentation for the specification and verification (LA4SV) of requirements on Dung’s abstract argumentation frameworks. We distinguish three kinds of decision problems for argumentation verification, called extension verification, framework verification, and specification verification respectively. For example, given a political requirement like “if the argument to increase taxes is accepted, then the argument to increase services must be accepted too,” we can either verify an extension of acceptable arguments, or all extensions of an argumentation framework, or all extensions of all argumentation frameworks satisfying a framework specification. We introduce the logic of argumentation verification to specify such requirements, and we represent the three verification problems of argumentation as model checking and theorem proving properties of the logic. Moreover, we recast the logic of argumentation verification in a modal framework, in order to express multiple extensions, and properties like transitivity and reflexivity of the attack relation. Finally, we introduce a logic of meta-argumentation where abstract argumentation is used to reason about abstract argumentation itself. We define the logic of meta-argumentation using the fibring methodology in such a way to represent attack relations not only among arguments but also among attacks. [less ▲] Detailed reference viewed: 96 (5 UL)Modelling defeasible and prioritized support in bipolar argumentation ; ; Gabbay, Dov M. et al in Annals of Mathematics & Artificial Intelligence (2012), 66(1-4), 163-197 Cayrol and Lagasquie-Schiex introduce bipolar argumentation frameworks by introducing a second relation on the arguments for representing the support among them. The main drawback of their approach is ... [more ▼] Cayrol and Lagasquie-Schiex introduce bipolar argumentation frameworks by introducing a second relation on the arguments for representing the support among them. The main drawback of their approach is that they cannot encode defeasible support, for instance they cannot model an attack towards a support relation. In this paper, we introduce a way to model defeasible support in bipolar argumentation frameworks. We use the methodology of meta-argumentation in which Dung’s theory is used to reason about itself. Dung’s well-known admissibility semantics can be used on this meta-argumentation framework to compute the acceptable arguments, and all properties of Dung’s classical theory are preserved. Moreover, we show how different contexts can lead to the alternative strengthening of the support relation over the attack relation, and converse. Finally, we present two applications of our methodology for modeling support, the case of arguments provided with an internal structure and the case of abstract dialectical frameworks. [less ▲] Detailed reference viewed: 82 (5 UL)Two dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones-Pörn deontic logic system] ; Gabbay, Dov M. ; Parent, Xavier et al in Synthese (2012), 187(2), 623--660 Detailed reference viewed: 84 (0 UL)Temporal, numerical and meta-level dynamics in argumentation networks ; Gabbay, Dov M. ; in Argument and Computation (2012), 3(2-3), 143--202 Detailed reference viewed: 53 (1 UL)Equational approach to argumentation networks Gabbay, Dov M. in Argument and Computation (2012), 3(2-3), 87--142 Detailed reference viewed: 58 (3 UL)Modal and temporal argumentation networks ; Gabbay, Dov M. ; in Argument and Computation (2012), 3(2-3), 203--227 Detailed reference viewed: 55 (1 UL) |
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