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1Frontiers of combining systems 2 (edited book)Research Studies Press. 2000.The International workshop 'Frontiers of Combining Systems' is the only forum that is exclusively devoted to research efforts in this interdisciplinary area. This volume contains selected, edited papers from the second installment of the workshop. The contributions range from theorem proving, rewriting and logic to systems and constraints. While there is a clear emphasis on automated tools and logics, the contributions to this volume show that there exists a rapidly expanding body of solutions o…Read more
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88Sequential Dynamic LogicJournal of Logic, Language and Information 21 (3): 279-298. 2012.We introduce a substructural propositional calculus of Sequential Dynamic Logic that subsumes a propositional part of dynamic predicate logic, and is shown to be expressively equivalent to propositional dynamic logic. Completeness of the calculus with respect to the intended relational semantics is established.
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17Products of modal logics and tensor products of modal algebrasJournal of Applied Logic 12 (4): 570-583. 2014.
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24A normal logic that is complete for neighborhood frames but not for Kripke framesTheoria 40 (3): 148-153. 1974.
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43Voting 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
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42Montague Type Semantics for Modal Logics with Propositional QuantifiersMathematical Logic Quarterly 17 (1): 245-249. 1971.
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120Direct deductive computation on discourse representation structuresLinguistics and Philosophy 17 (4). 1994.
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67A general theory of structured consequence relationsTheoria 10 (2): 49-78. 1995.There are several areas in logic where the monotonicity of the consequence relation fails to hold. Roughly these are the traditional non-monotonic systems arising in Artificial Intelligence (such as defeasible logics, circumscription, defaults, ete), numerical non-monotonic systems (probabilistic systems, fuzzy logics, belief functions), resource logics (also called substructural logics such as relevance logic, linear logic, Lambek calculus), and the logic of theory change (also called belief re…Read more
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3This volume constitutes the proceedings of the First International Conference on Temporal Logic (ICTL '94), held at Bonn, Germany in July 1994. Since its conception as a discipline thirty years ago, temporal logic is studied by many researchers of numerous backgrounds; presently it is in a stage of accelerated dynamic growth. This book, as the proceedings of the first international conference particularly dedicated to temporal logic, gives a thorough state-of-the-art report on all aspects of tem…Read more
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64Logical Modes of Attack in Argumentation NetworksStudia Logica 93 (2): 199-230. 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 the nodes in a network. General properties of logics are refined both in the object level and in the metalevel 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-bas…Read more
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106Adding a temporal dimension to a logic systemJournal of Logic, Language and Information 1 (3): 203-233. 1992.We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with Since and Until) in a special way. We refer to this method as adding a temporal dimension to L or just temporalising L. We show that the logic system T(L) preserves several properties of the original temporal logic like soundness, completeness, …Read more
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53Second-Order Quantifier Elimination in Higher-Order Contexts with Applications to the Semantical Analysis of ConditionalsStudia Logica 87 (1): 37-50. 2007.Second-order quantifier elimination in the context of classical logic emerged as a powerful technique in many applications, including the correspondence theory, relational databases, deductive and knowledge databases, knowledge representation, commonsense reasoning and approximate reasoning. In the current paper we first generalize the result of Nonnengart and Szałas [17] by allowing second-order variables to appear within higher-order contexts. Then we focus on a semantical analysis of conditio…Read more
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7Do we really need tenses other than future and past?In Rainer Bäuerle, Urs Egli & Arnim von Stechow (eds.), Semantics From Different Points of View, Springer Verlag. pp. 15--20. 1979.
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94Combining Temporal Logic SystemsNotre Dame Journal of Formal Logic 37 (2): 204-232. 1996.This paper investigates modular combinations of temporal logic systems. Four combination methods are described and studied with respect to the transfer of logical properties from the component one-dimensional temporal logics to the resulting combined two-dimensional temporal logic. Three basic logical properties are analyzed, namely soundness, completeness, and decidability. Each combination method comprises three submethods that combine the languages, the inference systems, and the semantics of…Read more
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55Handbook of the logic of argument and inference: the turn towards the practical (edited book)Elsevier. 2002.The Handbook of the Logic of Argument and Inference is an authoritative reference work in a single volume, designed for the attention of senior undergraduates, graduate students and researchers in all the leading research areas concerned with the logic of practical argument and inference. After an introductory chapter, the role of standard logics is surveyed in two chapters. These chapters can serve as a mini-course for interested readers, in deductive and inductive logic, or as a refresher. The…Read more
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15Two dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones–Pörn deontic logic system]Synthese 187 (2): 623-660. 2012.This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a detailed case study i…Read more
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78Semantics for Higher Level Attacks in Extended Argumentation Frames Part 1: OverviewStudia Logica 93 (2-3). 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 (of extensions) to such networks. We offer three different approaches to obtaining semantics. 1. The translation approach This uses the m…Read more
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43Craig interpolation theorem for intuitionistic logic and extensions part IIIJournal of Symbolic Logic 42 (2): 269-271. 1977.
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88Two dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones–Pörn deontic logic system]Synthese 187 (2): 623-660. 2012.This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a detailed case study i…Read more
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15A practical logic of cognitive systemsNorth Holland. 2003.Agenda Relevance is the first volume in the authors' omnibus investigation of the logic of practical reasoning, under the collective title, A Practical Logic of Cognitive Systems. In this highly original approach, practical reasoning is identified as reasoning performed with comparatively few cognitive assets, including resources such as information, time and computational capacity. Unlike what is proposed in optimization models of human cognition, a practical reasoner lacks perfect information,…Read more
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31Fibring logicsClarendon Press. 1999.Modern applications of logic in mathematics, computer science, and linguistics use combined systems of different types of logic working together. This book develops a method for combining--or fibring--systems by breaking them into simple components which can be manipulated easily and recombined.
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77A Meta-model of Access Control in a Fibred Security LanguageStudia Logica 92 (3): 437-477. 2009.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…Read more
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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.
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56A Logical Account of Formal ArgumentationStudia Logica 93 (2-3): 383-403. 2009.In this paper, we prove the correspondence between complete extensions in abstract argumentation and 3-valued stable models in logic programming. This result is in line with earlier work of [6] that identified the correspondence between the grounded extension in abstract argumentation and the well-founded model in logic programming, as well as between the stable extensions in abstract argumentation and the stable models in logic programming
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80An irreflexivity lemma with applications to axiomatizations of conditions on tense framesIn U. Mönnich (ed.), Aspects of Philosophical Logic, Dordrecht. pp. 67--89. 1981.