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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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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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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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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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69Expressive functional completeness in tense logic (preliminary report)In Uwe Mönnich (ed.), Aspects of Philosophical Logic: Some Logical Forays Into Central Notions of Linguistics and Philosophy, Dordrecht. pp. 91--117. 1981.
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99Montague Type Semantics for Modal Logics with Propositional QuantifiersMathematical Logic Quarterly 17 (1): 245-249. 1971.
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147Defeasible inheritance systems and reactive diagramsLogic Journal of the IGPL 17 (1): 1-54. 2008.Inheritance diagrams are directed acyclic graphs with two types of connections between nodes: x → y and x ↛ y . Given a diagram D, one can ask the formal question of “is there a valid path between node x and node y?” Depending on the existence of a valid path we can answer the question “x is a y” or “x is not a y”. The answer to the above question is determined through a complex inductive algorithm on paths between arbitrary pairs of points in the graph. This paper aims to simplify and interpret…Read more
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103Labelled deductive systemsOxford University Press. 1996.This important book provides a new unifying methodology for logic. It replaces the traditional view of logic as manipulating sets of formulas with the notion of structured families of labelled formulas with algebraic structures. This approach has far reaching consequences for the methodology of logics and their semantics, and the book studies the main features of such systems along with their applications. It will interest logicians, computer scientists, philosophers and linguists.
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88On modal logics characterized by models with relative accessibility relations: Part IIStudia Logica 66 (3): 349-384. 2000.This work is divided in two papers (Part I and Part II). In Part I, we introduced the class of Rare-logics for which the set of terms indexing the modal operators are hierarchized in two levels: the set of Boolean terms and the set of terms built upon the set of Boolean terms. By investigating different algebraic properties satisfied by the models of the Rare-logics, reductions for decidability were established by faithfully translating the Rare-logics into more standard modal logics (some of th…Read more
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106Łukasiewicz Logic: From Proof Systems To Logic ProgrammingLogic Journal of the IGPL 13 (5): 561-585. 2005.We present logic programming style “goal-directed” proof methods for Łukasiewicz logic Ł that both have a logical interpretation, and provide a suitable basis for implementation. We introduce a basic version, similar to goal-directed calculi for other logics, and make refinements to improve efficiency and obtain termination. We then provide an algorithm for fuzzy logic programming in Rational Pavelka logic RPL, an extension of Ł with rational constants
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1Handbook of Philosophical Logic, 2nd Edition, Volume 5Tijdschrift Voor Filosofie 65 (1): 184-185. 2003.
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77Semantical Investigations in Heyting's Intuitionistic LogicJournal of Symbolic Logic 51 (3): 824-824. 1986.
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87Handbook 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 ...
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14KM99] GP Kogan and JA Makowsky. Computing Schur functions for Borchardt matrices. in preparation, 1999. Kog96] GP Kogan. Computing the permanent over elds of characteristic 3: Where and why it becomes dificult. In FOCS'96, pages 108 {114. IEEE, 1996 (review)Annals of Pure and Applied Logic 78 (2): 189-202. 1996.
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39Representation of the Montague Semantics as a Form of the Suppes Semantics with Applications to the Problem of the Introduction of the Passive Voice, the Tenses, and Negation as TransformationsIn Patrick Suppes, Julius Moravcsik & Jaakko Hintikka (eds.), Approaches to Natural Language, Dordrecht. pp. 395--409. 1973.
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80Applications of Scott's notion of consequence to the study of general binary intensional connectives and entailmentJournal of Philosophical Logic 2 (3). 1973.
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154Voting 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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220Fibring Argumentation FramesStudia Logica 93 (2-3): 231-295. 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 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 theo…Read more
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107Products 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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40A General Theory of Structured Consequence RelationsTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 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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146Cut and payJournal of Logic, Language and Information 15 (3): 195-218. 2006.In this paper we study families of resource aware logics that explore resource restriction on rules; in particular, we study the use of controlled cut-rule and introduce three families of parameterised logics that arise from different ways of controlling the use of cut. We start with a formulation of classical logic in which cut is non-eliminable and then impose restrictions on the use of cut. Three Cut-and-Pay families of logics are presented, and it is shown that each family provides an approx…Read more