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149Undecidability of modal and intermediate first-order logics with two individual variablesJournal of Symbolic Logic 58 (3): 800-823. 1993.
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209Fibred 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
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228A theory of hypermodal logics: Mode shifting in modal logic (review)Journal of Philosophical Logic 31 (3): 211-243. 2002.A hypermodality is a connective □ whose meaning depends on where in the formula it occurs. The paper motivates the notion and shows that hypermodal logics are much more expressive than traditional modal logics. In fact we show that logics with very simple K hypermodalities are not complete for any neighbourhood frames
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175Neural-Symbolic Cognitive ReasoningSpringer. 2009.Humans are often extraordinary at performing practical reasoning. There are cases where the human computer, slow as it is, is faster than any artificial intelligence system. Are we faster because of the way we perceive knowledge as opposed to the way we represent it? The authors address this question by presenting neural network models that integrate the two most fundamental phenomena of cognition: our ability to learn from experience, and our ability to reason from what has been learned. This b…Read more
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55Compiled Labelled Deductive Systems: A Uniform Presentation of Non-classical LogicsInstitute of Physics/Research Studies Press. 2004.K. Broda, Dov M. Gabbay, Alessandra Russo and LuÍs C. Lamb argue that though the many families of logic may seem to differ in their logical nature, it is possible to provide them with a unifying logical framework whenever their semantics is axiomatizable in first-order logic. They provide such a framework based on the labeled deductive system methodology, and demonstrate how it works in such families as normal modal logics, conditional logics of normality, the modal logic of elsewhere, the multi…Read more
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260Roadmap for preferential logicsJournal of Applied Non-Classical Logics 19 (1): 43-95. 2009.We give a systematic overview of semantical and logical rules in non monotonic and related logics. We show connections and sometimes subtle differences, and also compare such rules to uses of the notion of size.
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85A normal logic that is complete for neighborhood frames but not for Kripke framesTheoria 41 (3): 148-153. 1975.
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33Frontiers 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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27Elementary Logics: A Procedural PerspectivePrentice-Hall. 1998.This text aims to introduce classical logic in such a way that one can also easily deviate into discussing non-classical logics. It defines the many types of logics and the differences between them, starting with the basic notions of the most common logic and working through the many non-classical logics.
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119On Kreisel's notion of validity in post systemsStudia Logica 35 (3). 1976.This paper investigates various interpretations of HPC (Heyting's predicate calculus) and mainly of HPC0 (Heyting's propositional calculus) in Post systems.§1 recalls some background material concerning HPC including the Kripke and Beth interpretations, and later sections study the various interpretations available.
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122The Functional Interpretation of the Existential QuantifierLogic Journal of the IGPL 3 (2-3): 243-290. 1995.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 ass…Read more
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146Decidability of some intuitionistic predicate theoriesJournal of Symbolic Logic 37 (3): 579-587. 1972.
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158Logical Modes of Attack in Argumentation NetworksStudia Logica 93 (2-3): 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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147Belief revision in non-classical logicsReview of Symbolic Logic 1 (3): 267-304. 2008.In this article, we propose a belief revision approach for families of (non-classical) logics whose semantics are first-order axiomatisable. Given any such (non-classical) logic , the approach enables the definition of belief revision operators for , in terms of a belief revision operation satisfying the postulates for revision theory proposed by Alchourrrdenfors and Makinson (AGM revision, Alchourrukasiewicz's many-valued logic. In addition, we present a general methodology to translate algebra…Read more
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88Calendar LogicJournal of Applied Non-Classical Logics 8 (4): 291-323. 1998.ABSTRACT A propositional temporal logic is introduced whose operators quantify over intervals of a reference time line. The intervals are specified symbolically, for example ?next week's weekend?. The specification language for the intervals takes into account all the features of real calendar systems. A simple statement which can be expressed in this language is for example: ?yesterday I worked for eight hours with one hour lunch break at noon?. Calendar Logic can be translated into proposition…Read more
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99Handbook 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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1An intuitionistic basis for non-monotonic reasoningIn Philippe Smets (ed.), Non-standard logics for automated reasoning, Academic Press. 1988.
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243Reactive preferential structures and nonmonotonic consequenceReview of Symbolic Logic 2 (2): 414-450. 2009.We introduce Information Bearing Relation Systems (IBRS) as an abstraction of many logical systems. These are networks with arrows recursively leading to other arrows etc. 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 the strong coherence properties of preferential structures by higher arrows, that is, arrows, w…Read more
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92A Structural Property On Modal Frames Characterizing Default LogicLogic Journal of the IGPL 4 (1): 7-22. 1996.We show that modal logics characterized by a class of frames satisfying the insertion property are suitable for Reiter's default logic. We refine the canonical fix point construction defined by Marek, Schwarz and Truszczyński for Reiter's default logic and thus we addrress a new paradigm for nonmonotonic logic. In fact, differently from the construction defined by these authors. we show that suitable modal logics for such a construction must indeed contain K D4. When reflexivity is added to the …Read more
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61Algorithms in cognition, informatics and logic: A position manifestoLogic Journal of the IGPL 18 (6): 763-768. 2010.
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160What is a logical system? (edited book)Oxford University Press. 1994.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, W…Read more
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66Fibring 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.