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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: 116 (4 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: 164 (0 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: 107 (4 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: 128 (5 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: 171 (0 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: 150 (6 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: 118 (0 UL)Arguing about the Trustworthiness of the Information Sources ; ; Gabbay, Dov M. et al in ECSQARU (2011) Trust minimizes the uncertainty in the interactions among the information sources. To express the possibly conflicting motivations about trust and distrust, we reason about trust using argumentation ... [more ▼] Trust minimizes the uncertainty in the interactions among the information sources. To express the possibly conflicting motivations about trust and distrust, we reason about trust using argumentation theory. First, we show how to model the sources and how to attack untrustworthy sources. Second, we provide a focused representation of trust about the sources in which trust concerns not only the sources but also the information items and the relation with other information. [less ▲] Detailed reference viewed: 156 (0 UL)Conditionals and Modularity in General Logics Gabbay, Dov M. ; Book published by Springer (2011) Detailed reference viewed: 94 (0 UL)Dung’s Argumentation is Essentially Equivalent to Classical Propositional Logic with the Peirce-Quine Dagger Gabbay, Dov M. in Logica Universalis (2011), 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– ... [more ▼] 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 ¬,∧,∨,→ 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 frames, predicate argumentation frames, etc., etc. We also offer the notion of logic proof as a geometrical walk along the nodes of a Dung network and thus we are able to offer a geometrical abstraction of the notion of inference based argumentation. Thus our paper is also a contribution to the question: “What is a logical system” in as much as it integrates logic with abstract argumentation networks [less ▲] Detailed reference viewed: 138 (0 UL)Introducing Equational Semantics for Argumentation Networks Gabbay, Dov M. in ECSQARU (2011) 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 ... [more ▼] 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, etc, etc. The equational approach has its conceptual roots in the 19th century following the algebraic equational approach to logic by George Boole, Louis Couturat and Ernst Schroeder. [less ▲] Detailed reference viewed: 106 (1 UL)Obligations and prohibitions in Talmudic deontic logic ; Gabbay, Dov M. ; in Artificial Intelligence and Law (2011), 19(2-3), 117148 Detailed reference viewed: 142 (1 UL)Reactive automata ; Gabbay, Dov M. in Information and Computation (2011), 209(4), 692704 A reactive automaton has extra links whose role is to change the behaviour of the automaton. We show that these links do not increase the expressiveness of finite automata but that they can be used to ... [more ▼] A reactive automaton has extra links whose role is to change the behaviour of the automaton. We show that these links do not increase the expressiveness of finite automata but that they can be used to reduce dramatically their state number both in the deterministic case and the non-deterministic case. Typical examples of regular expressions associated with deterministic automata of ex- ponential size according to the length of the expression show that reactive links provide an alternative representation of total linear size for the language [less ▲] Detailed reference viewed: 61 (1 UL)Reactive intuitionistic tableaux Gabbay, Dov M. in Synthese (2011), 179(2), 253269 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 Detailed reference viewed: 103 (0 UL)Argumentative Agents Negotiating on Potential Attacks ; Gabbay, Dov M. ; et al in KES-AMSTA (2011) When arguing, agents may want to discuss about the details after agreeing about the general problems. We propose to model this kind of situation using an extended argumentation framework with potential ... [more ▼] When arguing, agents may want to discuss about the details after agreeing about the general problems. We propose to model this kind of situation using an extended argumentation framework with potential attacks. Agents negotiation about raising potential attacks or not, in order to maximize the number of their accepted arguments. The result of the negotiation process consists in the formation of coalitions composed by those agents which have found an agreement. The two proposed negotiation protocols have been implemented and an evaluation, addressed by means of experimental results, shows which combination of strategies and negotiation protocol allows the agents to optimize outcomes. [less ▲] Detailed reference viewed: 114 (1 UL)Non-Deductive Inference in the Talmud Gabbay, Dov M. ; ; Book published by College Publications (2010) Detailed reference viewed: 59 (0 UL)Coalition Formation via Negotiation in Multiagent Systems with Voluntary Attacks ; Gabbay, Dov M. ; et al in Proceedings of the 22th Belgian-Netherlands Conference on Artificial Intelligence (BNAIC'10) (2010) Argumentation networks are put forward by Dung considering only one kind of attack among argu- ments. In this paper, we propose to extend Dung’s argumentation framework with voluntary attacks in the ... [more ▼] Argumentation networks are put forward by Dung considering only one kind of attack among argu- ments. In this paper, we propose to extend Dung’s argumentation framework with voluntary attacks in the context of multiagent systems, characterized by the possibility of the attacker to decide whether to attack or not. Enabling voluntary attacks impacts on the acceptability of the arguments in the framework, and therefore it becomes subject of debate between the agents. Agents can negotiate about which subset of voluntary attacks can be raised, and they form coalitions after the negotiation process. [less ▲] Detailed reference viewed: 23 (1 UL)Subsumption and Count as Relation in Arguments Ontologies ; Gabbay, Dov M. ; in Proceedings of the 13th International Workshop on Non-Monotonic Reasoning (NMR'10) (2010) The paper proposes a representation of the subsumption re- lation and of count as conditional in the context of argument ontologies. Starting from the weaker notion of classification represented by the ... [more ▼] The paper proposes a representation of the subsumption re- lation and of count as conditional in the context of argument ontologies. Starting from the weaker notion of classification represented by the subsumption relation towards the stronger notion of count as, we show how to reason whether an argu- ment is accepted in ontologies involving these two notions. We adopt the methodology of meta-argumentation in order to model the design decisions. Argumentation, being able to handle contradictory information, is proposed as technique to reason about count as for ontology interoperability. [less ▲] Detailed reference viewed: 33 (1 UL)A Theory of Hierarchical Consequence and Conditionals Gabbay, Dov M. ; in Journal of Logic, Language and Information (2010), 19(1), 332 We introduce A-ranked preferential structures and combine them with an accessibility relation. A-ranked preferential structures are intermediate between sim- ple preferential structures and ranked ... [more ▼] We introduce A-ranked preferential structures and combine them with an accessibility relation. A-ranked preferential structures are intermediate between sim- ple preferential structures and ranked structures. The additional accessibility relation allows us to consider only parts of the overall A-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. [less ▲] Detailed reference viewed: 112 (0 UL)A Comment on Work by Booth and Co-authors Gabbay, Dov M. ; in Studia Logica (2010), 94(3), 403432 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, < and, where < is the usual ranked relation, and is a sub ... [more ▼] 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, < and, where < is the usual ranked relation, and is a sub-relation of <. They have, however, left open a characterization of the infinite case, which we treat here. [less ▲] Detailed reference viewed: 132 (0 UL) |
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