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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: 27 (0 UL)Obligations and prohibitions in Talmudic deontic logic ; Gabbay, Dov M. ; in Artificial Intelligence & Law (2011), 19(2-3), 117148 Detailed reference viewed: 24 (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: 26 (1 UL)Conditionals and Modularity in General Logics Gabbay, Dov M. ; Book published by Springer (2011) Detailed reference viewed: 10 (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: 29 (0 UL)Reactive automata ; Gabbay, Dov M. in Information & 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: 11 (0 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: 16 (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: 23 (1 UL)Non-Deductive Inference in the Talmud Gabbay, Dov M. ; ; Book published by College Publications (2010) Detailed reference viewed: 14 (0 UL)Obligations and Prohibitions in Talmudic Deontic Logic ; Gabbay, Dov M. ; in DEON (2010) 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: OTA Talmudic obligation FTA Talmudic ... [more ▼] 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: OTA Talmudic obligation FTA Talmudic prohibition FDA Standard deontic prohibition ODA Standard deontic obligation [less ▲] Detailed reference viewed: 21 (0 UL)Subsumption and Count as Relation in Arguments Ontologies ; Gabbay, Dov M. ; in Procs. 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: 11 (0 UL)Modal Access Control Logic - Axiomatization, Semantics and FOl Theorem Proving Genovese, Valerio ; ; Gabbay, Dov M. et al in STAIRS 2010 (2010) We present and study a Modal Access Control Logic (M-ACL) to specify and reason about access control policies. We identify canonical properties of well-known access control axioms. We provide a Hilbert ... [more ▼] We present and study a Modal Access Control Logic (M-ACL) to specify and reason about access control policies. We identify canonical properties of well-known access control axioms. We provide a Hilbert-style proof-system and we prove soundness, completeness and decidability of the logic. We present a sound and complete embedding of Modal Access Control Logic into First-Order Logic. We show how to use SPASS theorem prover to reason about access control policies expressed as formulas of Modal Access Control Logic, and we compare our logic with existing ones. [less ▲] Detailed reference viewed: 22 (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: 27 (0 UL)Higher-Order Coalition Logic Boella, Guido ; Gabbay, Dov M. ; Genovese, Valerio et al in Bibliothèque(s) : revue de l'Association des bibliothécaires de France (2010) We introduce and study higher-order coalition logic, a multi modal monadic second-order logic with operators [{x}ψ]φ expressing that the coalition of all agents satisfying ψ(x) can achieve a state in ... [more ▼] We introduce and study higher-order coalition logic, a multi modal monadic second-order logic with operators [{x}ψ]φ expressing that the coalition of all agents satisfying ψ(x) can achieve a state in which φ holds. We use neighborhood semantics to model extensive games of perfect information with simultaneous actions and we provide a framework reasoning about agents in the same way as it is reasoning about their abilities. We illustrate higher-order coalition logic to represent and reason about coalition formation and cooperation, we show a more general and expressive way to quantify over coalitions than quantified coalition logic, we give an axiomatization and prove completeness. [less ▲] Detailed reference viewed: 17 (0 UL)Coalition Formation via Negotiation in Multiagent Systems with Voluntary Attacks ; Gabbay, Dov M. ; et al in Procs. 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: 11 (0 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: 34 (0 UL)Support in Abstract Argumentation Boella, Guido ; Gabbay, Dov M. ; van der Torre, Leon et al in Proceedings of the Third International Conference on Computational Models of Argument (COMMA'10) (2010) n this paper, we consider two drawbacks of Cayrol and Lagasque-Schiex's meta-argumentation theory to model bipolar argumentation frameworks. We consider first the “lost of admissibility” in Dung's sense ... [more ▼] n this paper, we consider two drawbacks of Cayrol and Lagasque-Schiex's meta-argumentation theory to model bipolar argumentation frameworks. We consider first the “lost of admissibility” in Dung's sense and second, the definition of notions of attack in the context of a support relation. We show how to prevent these drawbacks by introducing support meta-arguments. Like the model of Cayrol and Lagasque-Schiex, our formalization confirms the use of meta-argumentation to reuse Dung's properties. We do not take a stance towards the usefulness of a support relation among arguments, though we show that if one would like to introduce them, it can be done without extending Dung's theory. Finally, we show how to use meta-argumentation to instantiate an argumentation framework to represent defeasible support. In this model of support, the support relation itself can be attacked. [less ▲] Detailed reference viewed: 66 (0 UL)Arguing about Trust in Multiagent Systems ; Boella, Guido ; Gabbay, Dov M. et al in Proceedings of the 11th Symposium on Artificial Intelligence of the Italian Association for Artificial Intelligence (AIIA'10) (2010) Trust in multiagent systems is used for seeking to minimize the uncertainty in the interactions among the agents. In this paper, we discuss how to use argumentation to reason about trust. Using the ... [more ▼] Trust in multiagent systems is used for seeking to minimize the uncertainty in the interactions among the agents. In this paper, we discuss how to use argumentation to reason about trust. Using the methodology of meta-argumentation, first we represent the source of the information from which the argument is constructed in the abstract argumentation framework capturing the fact that b is attacked because b is from a particular source s. We show how a source of information can be attacked if it is not evaluated as trustworthy. Second, we provide a fine grained representation of the trust relationships between the information sources in which trust concerns not only the sources but also the single arguments and attack relations the sources propose. Moreover, we represent the evidences in support of the arguments which are put forward by the information sources and the agents can express arguments by referring to other agents’ arguments. Meta-argumentation allows us not to extend Dung’s abstract argumentation framework by introducing trust and to reuse those principles and properties defined for Dung’s framework. [less ▲] Detailed reference viewed: 15 (0 UL)Modal Logics of Reactive Frames Gabbay, Dov M. ; in Studia Logica (2009) A reactive graph generalizes the concept of a graph by making it dynamic, in the sense that the arrows coming out from a point depend on how we got there. This idea was fi rst applied to Kripke semantics ... [more ▼] A reactive graph generalizes the concept of a graph by making it dynamic, in the sense that the arrows coming out from a point depend on how we got there. This idea was fi rst applied to Kripke semantics of modal logic in [2]. In this paper we strengthen that unimodal language by adding a second operator. One op- erator corresponds to the dynamics relation and the other one relates paths with the same endpoint. We explore the expressivity of this interpretation by axiomatizing some natural subclasses of reactive frames. The main objective of this paper is to present a methodology to study reactive logics using the existent classic techniques. [less ▲] Detailed reference viewed: 21 (0 UL)Modal Foundations for Argumentation Networks Gabbay, Dov M. in Studia Logica (2009) Detailed reference viewed: 8 (0 UL) |
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