-
48Semantics for Higher Level Attacks in Extended Argumentation Frames Part 1: OverviewStudia Logica 93 (2-3): 181-198. 2009.Given an argumentation network we associate with it a modal formula representing the 'logical content' of the network. We show a one-to-one correspondence between all possible complete Caminada labellings of the network and all possible models of the formula
-
47Craig interpolation theorem for intuitionistic logic and extensions part IIIJournal of Symbolic Logic 42 (2): 269-271. 1977.
-
47Fibred semantics and the weaving of logics part 1: Modal and intuitionistic logicsJournal of Symbolic Logic 61 (4): 1057-1120. 1996.This is Part 1 of a paper on fibred semantics and combination of logics. It aims to present a methodology for combining arbitrary logical systems L i , i ∈ I, to form a new system L I . The methodology `fibres' the semantics K i of L i into a semantics for L I , and `weaves' the proof theory (axiomatics) of L i into a proof system of L I . There are various ways of doing this, we distinguish by different names such as `fibring', `dovetailing' etc, yielding different systems, denoted by L F I , L…Read more
-
46Fibred Security LanguageStudia Logica 92 (3): 395-436. 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 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 prov…Read more
-
46Sufficient conditions for the undecidability of intuitionistic theories with applicationsJournal of Symbolic Logic 37 (2): 375-384. 1972.
-
45Algorithmic proof methods and cut elimination for implicational logics part I: Modal implicationStudia Logica 61 (2): 237-280. 1998.In this work we develop goal-directed deduction methods for the implicational fragment of several modal logics. We give sound and complete procedures for strict implication of K, T, K4, S4, K5, K45, KB, KTB, S5, G and for some intuitionistic variants. In order to achieve a uniform and concise presentation, we first develop our methods in the framework of Labelled Deductive Systems [Gabbay 96]. The proof systems we present are strongly analytical and satisfy a basic property of cut admissibility.…Read more
-
45Reactive intuitionistic tableauxSynthese 179 (2): 253-269. 2011.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
-
45Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol 3 (edited book)Kluwer Academic. 1998.HANDBOOK OF DEFEASIBLE REASONING AND UNCERTAINTY MANAGEMENT SYSTEMS EDITORS: DOV M. ... and A. Hunter Volume 3: Belief Change Edited by D. Dubois and H. Prade HANDBOOK OF DEFEASIBLE REASONING AND ...
-
45Voting by Eliminating QuantifiersStudia Logica 92 (3): 365-379. 2009.Mathematical theory of voting and social choice has attracted much attention. 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 ra…Read more
-
44Size and logicReview of Symbolic Logic 2 (2): 396-413. 2009.We show how to develop a multitude of rules of nonmonotonic logic from very simple and natural notions of size, using them as building blocks
-
44Undecidability of modal and intermediate first-order logics with two individual variablesJournal of Symbolic Logic 58 (3): 800-823. 1993.
-
44The Talmudic Logic Project, Ongoing Since 2008Logica Universalis 13 (4): 425-442. 2019.We describe the state of the Talmudic Logic project as of end of 2019. The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components centuries ahead of their time. In many cases the basic principles are not explicitly formulated, which makes it difficult to formalize and make available to the modern student of Logic. This project on Talmudic Logic, aims to present logical analysis of Talmudic reasoning using modern logical tools…Read more
-
43Montague Type Semantics for Modal Logics with Propositional QuantifiersMathematical Logic Quarterly 17 (1): 245-249. 1971.
-
42Temporal Logic: Mathematical Foundations and Computational AspectsOxford University Press on Demand. 1994.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 inclusio…Read more
-
41Products of modal logics, part 1Logic Journal of the IGPL 6 (1): 73-146. 1998.The paper studies many-dimensional modal logics corresponding to products of Kripke frames. It proves results on axiomatisability, the finite model property and decidability for product logics, by applying a rather elaborated modal logic technique: p-morphisms, the finite depth method, normal forms, filtrations. Applications to first order predicate logics are considered too. The introduction and the conclusion contain a discussion of many related results and open problems in the area
-
41Temporal, numerical and meta-level dynamics in argumentation networksArgument and Computation 3 (2-3). 2012.This paper studies general numerical networks with support and attack. Our starting point is argumentation networks with the Caminada labelling of three values 1=in, 0=out and ½=undecided. This is generalised to arbitrary values in [01], which enables us to compare with other numerical networks such as predator?prey ecological networks, flow networks, logical modal networks and more. This new point of view allows us to see the place of argumentation networks in the overall landscape of networks …Read more
-
40The decision problem for some finite extensions of the intuitionistic theory of abelian groupsStudia Logica 34 (1): 59-67. 1975.
-
39Completeness properties of heyting's predicate calculus with respect to re modelsJournal of Symbolic Logic 41 (1): 81-94. 1976.
-
39Equational approach to argumentation networksArgument and Computation 3 (2-3). 2012.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, and much more. The equational appr…Read more
-
39Future determination of entities in Talmudic public announcement logicJournal of Applied Logic 11 (1): 63-90. 2013.
-
38Semantics for Higher Level Attacks in Extended Argumentation Frames Part 1: OverviewStudia Logica 93 (2-3): 357-381. 2009.In 2005 the author introduced networks which allow attacks on attacks of any level. So if a → b reads a attacks 6, 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 to such networks. We offer three different approaches to obtaining semantics. 1. The translation approach This uses the methodology of ' …Read more
-
38Semantic interpolationJournal of Applied Non-Classical Logics 20 (4): 345-371. 2010.The problem of interpolation is a classical problem in logic. Given a consequence relation |~ and two formulas φ and ψ with φ |~ ψ we try to find a “simple" formula α such that φ |~ α |~ ψ. “Simple" is defined here as “expressed in the common language of φ and ψ". Non-monotonic logics like preferential logics are often a mixture of a non-monotonic part with classical logic. In such cases, it is natural examine also variants of the interpolation problem, like: is there “simple" α such that φ ⊢ α …Read more
-
38Decidability of some intuitionistic predicate theoriesJournal of Symbolic Logic 37 (3): 579-587. 1972.
-
37Products of modal logics. Part 3: Products of modal and temporal logicsStudia Logica 72 (2): 157-183. 2002.In this paper we improve the results of [2] by proving the product f.m.p. for the product of minimal n-modal and minimal n-temporal logic. For this case we modify the finite depth method introduced in [1]. The main result is applied to identify new fragments of classical first-order logic and of the equational theory of relation algebras, that are decidable and have the finite model property.
-
37A theory of hierarchical consequence and conditionalsJournal of Logic, Language and Information 19 (1): 3-32. 2010.We introduce -ranked preferential structures and combine them with an accessibility relation. -ranked preferential structures are intermediate between simple preferential structures and ranked structures. The additional accessibility relation allows us to consider only parts of the overall -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. Repre…Read more
-
36Annotation Theories over Finite GraphsStudia Logica 93 (2): 147-180. 2009.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 annotati…Read more