-
15Extending the Curry-Howard Interpretation to Linear, Relevant and Other Resource LogicsJournal of Symbolic Logic 57 (4). 1992.
-
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
-
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
-
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
-
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
-
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
-
J. EL1ASSON Ultrapowers as sheaves on a category of ultrafilters 825 A. LEWIS Finite cupping sets 845Archive for Mathematical Logic 43 (7): 934. 2004.
-
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
-
58A 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
-
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
-
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
-
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 ...
-
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.
-
51A normal logic that is complete for neighborhood frames but not for Kripke framesTheoria 41 (3): 148-153. 1975.
-
66Uncertainty Rules in Talmudic ReasoningHistory and Philosophy of Logic 32 (1): 63-69. 2011.The Babylonian Talmud, compiled from the 2nd to 7th centuries C.E., is the primary source for all subsequent Jewish laws. It is not written in apodeictic style, but rather as a discursive record of (real or imagined) legal (and other) arguments crossing a wide range of technical topics. Thus, it is not a simple matter to infer general methodological principles underlying the Talmudic approach to legal reasoning. Nevertheless, in this article, we propose a general principle that we believe helps …Read more
-
88Fuzzy logics based on [0,1)-continuous uninormsArchive for Mathematical Logic 46 (5-6): 425-449. 2007.Axiomatizations are presented for fuzzy logics characterized by uninorms continuous on the half-open real unit interval [0,1), generalizing the continuous t-norm based approach of Hájek. Basic uninorm logic BUL is defined and completeness is established with respect to algebras with lattice reduct [0,1] whose monoid operations are uninorms continuous on [0,1). Several extensions of BUL are also introduced. In particular, Cross ratio logic CRL, is shown to be complete with respect to one special …Read more
-
6Modelling evolvable component systems: Part I: A logical frameworkLogic Journal of the IGPL 17 (6): 631-696. 2009.We develop a logical modelling approach to describe evolvable computational systems. In this account, evolvable systems are built hierarchically from components where each component may have an associated supervisory process. The supervisor's purpose is to monitor and possibly change its associated component. Evolutionary change may be determined purely internally from observations made by the supervisor or may be in response to external change. Supervisory processes may be present at any level …Read more
-
46Products of modal logics, part 1Logic Journal of the IGPL 6 (1): 73-146. 1998.The paper studies many-dimensional modal logics corresponding to products of Kripke frames. It proves results on axiomatisability, the finite model property and decidability for product logics, by applying a rather elaborated modal logic technique: p-morphisms, the finite depth method, normal forms, filtrations. Applications to first order predicate logics are considered too. The introduction and the conclusion contain a discussion of many related results and open problems in the area
-
13Elementary 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.
-
23Model Theory for Intuitionistic LogicZeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (4-6): 49-54. 1972.
-
Sampling Logic and Argumentation Networks: A ManifestoJournal of the Indian Council of Philosophical Research 27 (2). 2010.
-
39Decidability of some intuitionistic predicate theoriesJournal of Symbolic Logic 37 (3): 579-587. 1972.