Dov Gabbay

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 ${\neg, \wedge, \vee, \to}$ 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

We are concerned with showing how ‘labelled’ Natural Deduction presentation systems based on an extension of the so-called Curry-Howard functional interpretation can help us understand and generalise most of the deduction calculi designed to deal with the logical notion of existential quantification. We present the labelling mechanism for ‘’ using what we call ‘ɛ-terms’, which have the form of ‘a’) in a dual form to the ‘Ax.f’ terms of in the sense that the ‘witness’ is chosen at the time of assertion/introduction.With the intention of demonstrating the generality of our framework, we provide a brief comparison with some other calculi of existentials, including the model-theoretic interpretations of Skolem and Herbrand, indicating the way in which some of the classical results on prenex normal forms can be extended to a wide range of logics. The essential ingredient is to look at the conceptual framework of labelled natural deduction as an attempted reconstruction of Frege's functional calculus where the devices of the Begriffsschrift work separately from, yet in harmony with, those of the Grundgesetze 1

In the current paper we consider theories with vocabulary containing a number 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, approximate 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 annotation 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]

This superb collection of papers focuses on a fundamental question in logic and computation: What is a logical system? With contributions from leading researchers--including Ian Hacking, Robert Kowalski, Jim Lambek, Neil Tennent, Arnon Avron, L. Farinas del Cerro, Kosta Dosen, and Solomon Feferman--the book presents a wide range of views on how to answer such a question, reflecting current, mainstream approaches to logic and its applications. Written to appeal to a diverse audience of readers, What is a Logical System? will excite discussion among students, teachers, and researchers in mathematics, logic, computer science, philosophy, and linguistics.

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.

This much-needed book provides a thorough account of temporal logic, one of the most important areas of logic in computer science today. The book begins with a solid introduction to semantical and axiomatic approaches to temporal logic. It goes on to cover predicate temporal logic, meta-languages, general theories of axiomatization, many dimensional systems, propositional quantifiers, expressive power, Henkin dimension, temporalization of other logics, and decidability results. With its inclusion of cutting-edge results and unifying methodologies, this book is an indispensable reference for both the pure logician and the theoretical computer scientist.

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 first applied to Kripke semantics of modal logic in [2]. In this paper we strengthen that unimodal language by adding a second operator. One operator 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