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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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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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47Fibred 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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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
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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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8Interactive Logic: Selected Papers From the 7th Augustus de Morgan Workshop, London (edited book)Amsterdam University Press. 2007.This collection of papers from the workshop serves as the initial volume in the new series Texts in Logics and Games—touching on research in logic, mathematics, computer science, and game theory. “A wonderful demonstration of ...
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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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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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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
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J. EL1ASSON Ultrapowers as sheaves on a category of ultrafilters 825 A. LEWIS Finite cupping sets 845Archive for Mathematical Logic 43 (7): 934. 2004.
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58On modal logics characterized by models with relative accessibility relations: Part IStudia Logica 65 (3): 323-353. 2000.This work is divided in two papers (Part I and Part II). In Part I, we study a class of polymodal logics (herein called 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 are established by faithfully translating the Rare-logics int…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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98Handbook of Philosophical Logic (edited book)Kluwer Academic Publishers. 1983.The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work ...
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146A Logical Account of Formal ArgumentationStudia Logica 93 (2-3): 109-145. 2009.In the current paper, we re-examine how abstract argumentation can be formulated in terms of labellings, and how the resulting theory can be applied in the field of modal logic. In particular, we are able to express the (complete) extensions of an argumentation framework as models of a set of modal logic formulas that represents the argumentation framework. Using this approach, it becomes possible to define the grounded extension in terms of modal logic entailment.
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86Reactive 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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23A Sound And Complete Deductive System For Ctl* VerificationLogic Journal of the IGPL 16 (6): 499-536. 2008.The paper presents a compositional approach to the verification of CTL* properties over reactive systems. Both symbolic model-checking and deductive verification are considered. Both methods are based on two decomposition principles. A general state formula is decomposed into basic state formulas which are CTL* formulas with no embedded path quantifiers. To deal with arbitrary basic state formulas, we introduce another reduction principle which replaces each basic path formula, i.e., path formul…Read more