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Normality, non-contamination and logical depth in classical natural deduction ; Gabbay, Dov M. ; in Studia Logica (2020), 108(2), 291--357 In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard ... [more ▼] In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard Gentzen-style natural deduction, (ii) admits of a simple normalization procedure such that normal proofs enjoy the Weak Subformula Property, (iii) provides the means to prove a Non-Contamination Property of normal proofs that is not satisfied by normal proofs in the Gentzen tradition and is useful for applications, especially to formal argumentation, (iv) naturally leads to defining a notion of depth of a proof, to the effect that, for every fixed natural k, normal k-depth deducibility is a tractable problem and converges to classical deducibility as k tends to infinity. [less ▲] Detailed reference viewed: 32 (0 UL)“Understanding Hohfeld and Formalizing Legal Rights: the Hohfeldian Conceptions and Their Conditional Consequences Markovich, Réka in Studia Logica (2019) Detailed reference viewed: 65 (3 UL)Modal definability based on Łukasiewicz validity relations Teheux, Bruno in Studia Logica (2016), 104(2), 343-363 Detailed reference viewed: 119 (8 UL)Extending Łukasiewicz Logics with a Modality: Algebraic Approach to Relational Semantics ; Teheux, Bruno in Studia Logica (2013), 101(3), 505-545 Detailed reference viewed: 219 (14 UL)An internal version of epistemic logic Aucher, Guillaume in Studia Logica (2010), 94(1), 1-22 Representing an epistemic situation involving several agents obviously depends on the modeling point of view one takes. We start by identifying the types of modeling points of view which are logically ... [more ▼] Representing an epistemic situation involving several agents obviously depends on the modeling point of view one takes. We start by identifying the types of modeling points of view which are logically possible. We call the one traditionally followed by epistemic logic the perfect external approach, because there the modeler is assumed to be an omniscient and external observer of the epistemic situation. In the rest of the paper we focus on what we call the internal approach, where the modeler is one of the agents involved in the situation. For this approach we propose and axiomatize a logical formalism based on epistemic logic. This leads us to formalize some intuitions about the internal approach and about its connections with the external ones. Finally, we show that our internal logic is decidable and PSPACE-complete. [less ▲] Detailed reference viewed: 117 (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: 102 (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: 91 (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: 76 (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: 90 (0 UL)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: 125 (2 UL)Meta-Argumentation part 1 Boella, Guido ; Gabbay, Dov M. ; van der Torre, Leon et al in Studia Logica (2009) In this paper, we introduce the methodology and techniques of meta-argumentation to model argumentation. The methodology of meta-argumentation instantiates Dung’s abstract argumentation theory with an ... [more ▼] In this paper, we introduce the methodology and techniques of meta-argumentation to model argumentation. The methodology of meta-argumentation instantiates Dung’s abstract argumentation theory with an extended argumentation theory, and is thus based on a combination of the methodology of instantiating abstract arguments, and the methodology of extending Dung’s basic argumentation frameworks with other relations among abstract arguments. The technique of meta-argumentation applies Dung’s theory of abstract argumentation to itself, by instantiating Dung’s abstract arguments with meta-arguments using a technique called flattening. We characterize the domain of instantiation using a representation technique based on soundness and completeness. Finally, we distinguish among various instantiations using the technique of specification languages. [less ▲] Detailed reference viewed: 40 (0 UL)Modal Foundations for Argumentation Networks Gabbay, Dov M. in Studia Logica (2009) Detailed reference viewed: 24 (0 UL)Voting with Second Order Quantifier Elimination Gabbay, Dov M. ; in Studia Logica (2009), 92(3), 365379 Detailed reference viewed: 17 (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: 40 (3 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: 126 (0 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: 67 (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: 96 (0 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: 99 (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: 92 (1 UL)Fibred security language ; ; Genovese, Valerio et al in Studia Logica (2009) We study access control policies based on the says operator by introducing a logical framework called Fibred Security Language (FSL) which is able to deal with features like joint responsibility between ... [more ▼] We study access control policies based on the says operator by introducing a logical framework called Fibred Security Language (FSL) which is able to deal with features like joint responsibility between sets of principals and to identify them by means of first-order formulas. FSL is based on a multimodal logic methodology. We first discuss the main contributions from the expressiveness point of view, we give semantics for the language both for classical and intuitionistic fragment), we then prove that in order to express well-known properties like ‘speaks-for’ or ‘hand-off’, defined in terms of says, we do not need second-order logic (unlike previous approaches) but a decidable fragment of first-order logic suffices. We propose a model-driven study of the says axiomatization by constraining the Kripke models in order to respect desirable security properties, we study how existing access control logics can be translated into FSL and we give completeness for the logic. [less ▲] Detailed reference viewed: 92 (3 UL) |
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