•  58
    On modal logics characterized by models with relative accessibility relations: Part I
    with Stéphane Demri
    Studia 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
  •  41
    Semantic interpolation
    with Karl Schlechta
    Journal 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
  •  4
    "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
  •  4
    Introduction
    with Fiora Pirri
    Studia Logica 59 (1): 1-4. 1997.
  •  98
    Handbook of Philosophical Logic (edited book)
    with Franz Guenthner
    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 ...
  •  146
    A Logical Account of Formal Argumentation
    with Martin W. A. Caminada
    Studia 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.
  •  86
    Reactive preferential structures and nonmonotonic consequence
    with Karl Schlechta
    Review 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
  •  23
    A Sound And Complete Deductive System For Ctl* Verification
    Logic 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
  •  88
    Fuzzy logics based on [0,1)-continuous uninorms
    with George Metcalfe
    Archive 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
  •  6
    Modelling evolvable component systems: Part I: A logical framework
    with Howard Barringer and David Rydeheard
    Logic 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
  •  46
    Products of modal logics, part 1
    Logic 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
  •  66
    Uncertainty Rules in Talmudic Reasoning
    with Moshe Koppel
    History 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
  •  13
    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.
  •  2
    Handbook of Logic in Computer Science (edited book)
    with S. Abramsky and T. Maibaurn
    Oxford University Press. 1992.
  •  23
    Model Theory for Intuitionistic Logic
    Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (4-6): 49-54. 1972.
  •  25
  •  70
    Labelled deductive systems
    Oxford 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.
  •  35
    Fibred semantics for feature-based grammar logic
    with Jochen Dörre and Esther König
    Journal of Logic, Language and Information 5 (3-4): 387-422. 1996.
    This paper gives a simple method for providing categorial brands of feature-based unification grammars with a model-theoretic semantics. The key idea is to apply the paradigm of fibred semantics (or layered logics, see Gabbay (1990)) in order to combine the two components of a feature-based grammar logic. We demonstrate the method for the augmentation of Lambek categorial grammar with Kasper/Rounds-style feature logic. These are combined by replacing (or annotating) atomic formulas of the first …Read more
  • Sampling Logic and Argumentation Networks: A Manifesto
    Journal of the Indian Council of Philosophical Research 27 (2). 2010.
  •  12
    Alternatives to Standard first-order Semantics
    with Hugues Leblanc and F. Guenthner
    Journal of Symbolic Logic 54 (4): 1483-1484. 1989.
  •  23
    Calendar Logic
    with Hans Jürgen Ohlbach
    Journal 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
  •  1
    Handbook of Philosophical Logic, 2nd Edition, Volume 5
    with Franz Guenthner
    Tijdschrift Voor Filosofie 65 (1): 184-185. 2003.
  •  23
    Journal of Applied Logic Special Volume on Neural-Symbolic Systems
    with Artur D'Avila Garcez, Steffen Hölldobler, and John G. Taylor
    Journal of Applied Logic 2 (3): 241-243. 2004.
  •  67
    Belief revision in non-classical logics
    with Odinaldo Rodrigues and Alessandra Russo
    Review 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
  •  46
    Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol 3 (edited book)
    with P. Smets
    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 ...