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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: 130 (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: 60 (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: 63 (1 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: 231 (1 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: 55 (0 UL)Independence-Revision and Defaults Gabbay, Dov M. ; in Studia Logica (2009), 92(3), 381394 We investigate different aspects of independence here, in th e context of theory revision, generalizing slightly work by Chopra, Parikh, and Rodrigues, and in the context of prefere ntial reasoning Detailed reference viewed: 111 (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: 111 (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: 124 (0 UL)Roadmap for Preferential Logics Gabbay, Dov M. ; in Journal of Applied Non-Classical Logics (2009), 19(1), 4395 Detailed reference viewed: 108 (0 UL)Analysis of the Talmudic Argumentum A Fortiori Inference Rule (Kal-Vachomer) using Matrix Abduction ; Gabbay, Dov M. ; in Studia Logica (2009), 92(3), 281364 We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Ana- logy and the rule of Argumentum A Fortiori ... [more ▼] We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Ana- logy and the rule of Argumentum A Fortiori. Given a matrix A with entries in {0,1},we allow for one or more blank squares in the matrix, say ai,j=?. The method allows us to decide whether to declare ai,j=0 or ai,j=1 or ai,j=? undecided. This algorithmic method is then applied to modelling several legal and practical reasoning situations including the Talmudic rule of Kal-Vachomer. We add an Appendix showing that this new rule of Matrix Abduction, arising from the Talmud, can also be applied to the analysis of paradoxes in voting and judgement aggregation. In fact we have here a general method for executing non-deductive inferences. [less ▲] Detailed reference viewed: 117 (0 UL)A Theory of Hierarchical Conditionals Gabbay, Dov M. ; in Journal of Logic, Language and Information (2009) Detailed reference viewed: 33 (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: 48 (3 UL)Annotation theories over finite graphs Gabbay, Dov M. ; in Studia Logica (2009) In the current paper we consider theories with vocabulary containing a num- ber of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations ... [more ▼] In the current paper we consider theories with vocabulary containing a num- ber of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations represent unique annotations of the graph’s nodes. Such theories, which we call annotation theories , can be used in many applications, including the formalization of argumentation, approxim ate reasoning, semantics of logic programs, graph coloring, etc. We address a number of problems related to annotation theories over finite models, including satisfiability, querying problem, specification of preferred models and model checking problem. We show that most of considered problems are NPTime -or co-NPTime -complete. In order to reduce the complexity for particular theories, we use second-order quantifier elimination. To our best knowledge none of existing methods works in the case of anno- tation theories. We then provide a new second-order quantifier elimination method for stratified theories, which is successful in the considered cases. The new result subsumes many other results, including those of [2, 28, 21]. [less ▲] Detailed reference viewed: 99 (0 UL)A meta-model of access control in a fibred security language ; ; Gabbay, Dov M. et al in Studia Logica (2009), 92(3), 437-477 The issue of representing access control requirements continues to demand significant attention. The focus of researchers has traditionally been on developing particular access control models and policy ... [more ▼] The issue of representing access control requirements continues to demand significant attention. The focus of researchers has traditionally been on developing particular access control models and policy specification languages for particular applications. However, this approach has resulted in an unnecessary surfeit of models and languages. In contrast, we describe a general access control model and a logic-based specification language from which both existing and novel access control models may be derived as particular cases and from which several approaches can be developed for domain-specific applications. We will argue that our general framework has a number of specific attractions and an implication of our work is to encourage a methodological shift from a study of the particulars of access control to its generalities. [less ▲] Detailed reference viewed: 157 (0 UL)An Analysis of Defeasible Inheritance Systems Gabbay, Dov M. ; in Logic Journal of the IGPL (2009) Detailed reference viewed: 93 (0 UL)Fallacies as Cognitive Virtues Gabbay, Dov M. ; in Logic, Games and Philosophy: Foundational Perspectives (2009) In its recent attention to reasoning that is agent-based and target-driven, logic has re-taken the practical turn and recovered something of its historic mission. In so doing, it has taken on in a quite ... [more ▼] In its recent attention to reasoning that is agent-based and target-driven, logic has re-taken the practical turn and recovered something of its historic mission. In so doing, it has taken on in a quite general way a game-theoretic character, precisely as it was with the theory of syllogistic refutation in the Topics and On Sophistical Refutations, where Aristotle develops winning strategies for disputations. The approach that the present authors take toward the logic of practical reasoning is one in which cognitive agency is inherently strategic in its orientation. In particular, as is typically the case, individual agents set cognitive targets for themselves opportunistically, that is, in such ways that the attainment of those targets can be met with resources currently or forseeably at their disposal. This not to say that human reasoning is so game-like as to be utterly tendentious. But it does make the point that the human player of the cognitive game has no general stake in accepting undertakings that he has no chance of making good on. Throughout its long history, the traditional fallacies have been characterized as mistakes that are attractive, universal and incorrigible. In the present essay, we want to begin developing an alternative understanding of the fallacies. We will suggest that, when they are actually employed by beings like us, they are defensible strategies in game-theoretically describable pursuit of cognitive (and other) ends. [less ▲] Detailed reference viewed: 85 (0 UL)Reactive Preferencial Structures and Nonmonotonic consequence Gabbay, Dov M. ; in Review of Symbolic Logic (2009) Detailed reference viewed: 30 (0 UL)Revision, Acceptability and Context Gabbay, Dov M. ; ; Book published by Springer (2009) Detailed reference viewed: 83 (0 UL)Quantification in Non-classical Logics Gabbay, Dov M. ; ; Book published by Elsevier (2009) Detailed reference viewed: 33 (0 UL)Reactive Preferential Structures and Nonmonotonic consequence Gabbay, Dov M. ; in Review of Symbolic Logic (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: 110 (1 UL) |
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