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36Expressive 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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Sampling logic and argumentationJournal of the Indian Council of Philosophical Research 28 (2): 233-255. 2010.
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15Defeasible 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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19Kripke Saul A.. Semantical considerations for modal logics. Proceedings of a Colloquium on Modal and Many-valued Logics, Helsinki, 23-26 August, 1962, Acta Philosophica Fennica 1963, pp. 83–94 (review)Journal of Symbolic Logic 34 (3): 501-501. 1969.
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11The Functional Interpretation of the Existential QuantifierLogic Journal of the IGPL 3 (2-3): 243-290. 1995.
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23Calendar 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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62A neural cognitive model of argumentation with application to legal inference and decision makingJournal of Applied Logic 12 (2): 109-127. 2014.Formal models of argumentation have been investigated in several areas, from multi-agent systems and artificial intelligence (AI) to decision making, philosophy and law. In artificial intelligence, logic-based models have been the standard for the representation of argumentative reasoning. More recently, the standard logic-based models have been shown equivalent to standard connectionist models. This has created a new line of research where (i) neural networks can be used as a parallel computati…Read more
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46Size 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
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27Applications 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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21Goal-directed proof theoryKluwer Academic. 2000.Goal Directed Proof Theory presents a uniform and coherent methodology for automated deduction in non-classical logics, the relevance of which to computer science is now widely acknowledged. The methodology is based on goal-directed provability. It is a generalization of the logic programming style of deduction, and it is particularly favourable for proof search. The methodology is applied for the first time in a uniform way to a wide range of non-classical systems, covering intuitionistic, inte…Read more
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37Fibred 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
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21Reactive 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
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15Extending the Curry-Howard Interpretation to Linear, Relevant and Other Resource LogicsJournal of Symbolic Logic 57 (4). 1992.
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18A 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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9A 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, numerical non-monotonic systems, resource logics, and the logic of theory change. We are seeking a common axiomatic and semantical approach to the notion of consequence whieh can be specialised to any of the above areas. This paper introduces the notions of structured consequence relation, shift operators an…Read more
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38A 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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90Many-dimensional modal logics: theory and applications (edited book)Elsevier North Holland. 2003.Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a…Read more
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18Equal Rights for the Cut: Computable Non-analytic Cuts in Cut-based ProofsLogic Journal of the IGPL 15 (5-6): 553-575. 2007.This work studies the structure of proofs containing non-analytic cuts in the cut-based system, a sequent inference system in which the cut rule is not eliminable and the only branching rule is the cut. Such sequent system is invertible, leading to the KE-tableau decision method. We study the structure of such proofs, proving the existence of a normal form for them in the form of a comb-tree proof. We then concentrate on the problem of efficiently computing non-analytic cuts. For that, we study …Read more
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41Semantic 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
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4Classical vs non-classical logics: the universality of classical logicMax-Planck-Institut für Informatik. 1993."This report investigates the question of the universality of classical logic. The approach is to show that an almost arbitrary logical system can be translated reasonably intuitively and almost automatically into classical logic. The path leading to this result goes through the analysis of what is reasonable logic, how to find semantics for it, how to build a labelled deductive system (LDS) for it, how to translate a LDS into classical logic and how to automate the process using SCAN. This repo…Read more