•  2
    Handbook of Logic in Computer Science (edited book)
    with S. Abramsky and T. Maibaurn
    Oxford University Press. 1992.
  •  47
    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
  • A tense system with split truth table
    Logique Et Analyse 20 (80): 359. 1977.
  •  29
    Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol 3 (edited book)
    with P. Smets
    Kluwer Academic. 1998.
  •  3
    Logic and cognition
    with H. Cowles, Matthew Walenski, Robert Kluender, Markus Knauff, Artur S. Davila Garcez, Oliver Ray, John Woods, Robin Clark, and Murray Grossman
    Topoi 26 (1): 51-62. 2007.
    We consider connections between number sense—the ability to judge number—and the interpretation of natural language quantifiers. In particular, we present empirical evidence concerning the neuroanatomical underpinnings of number sense and quantifier interpretation. We show, further, that impairment of number sense in patients can result in the impairment of the ability to interpret sentences containing quantifiers. This result demonstrates that number sense supports some aspects of the language …Read more
  •  18
    Model Theory for Intuitionistic Logic
    Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (4-6): 49-54. 1972.
  •  11
    Agenda Relevance is the first volume in the authors' omnibus investigation of the logic of practical reasoning, under the collective title, A Practical Logic of Cognitive Systems. In this highly original approach, practical reasoning is identified as reasoning performed with comparatively few cognitive assets, including resources such as information, time and computational capacity. Unlike what is proposed in optimization models of human cognition, a practical reasoner lacks perfect information,…Read more
  • Sampling logic and argumentation
    Journal of the Indian Council of Philosophical Research 28 (2): 233-255. 2010.
  •  19
    Fibring Logics
    Clarendon Press. 1999.
    Modern applications of logic in mathematics, computer science, and linguistics use combined systems of different types of logic working together. This book develops a method for combining--or fibring--systems by breaking them into simple components which can be manipulated easily and recombined.
  •  7
    A Language For Handling Hypothetical Updates And Inconsistency
    with Laura Giordano, Alberto Martelli, and Nicola Olivetti
    Logic Journal of the IGPL 4 (3): 385-416. 1996.
    In this paper we propoee a logic programming language which supports hypothetical updates together with integrity constraints. The language makes use of a revision mechanism, which is needed to restore consistency when an update violates some integrity constraint. The revision policy adopted is based on the simple idea that more recent information is preferred to earlier one. We show how this language can be used to represent and perform several types of defeasible reasoning. We develop a logica…Read more
  •  34
    Complete Extensions in Argumentation Coincide with 3-Valued Stable Models in Logic Programming
    with Yining Wu and Martin Caminada
    Studia Logica 93 (2): 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
  •  45
    Meta-Argumentation Modelling I: Methodology and Techniques
    with Guido Boella, Dov M. Gabbay, Leendert van der Torre, and Serena Villata
    Studia Logica 93 (2-3). 2009.
    In this paper, we introduce the methodology and techniques of metaargumentation to model argumentation. The methodology of meta-argumentation instantiates Dung's abstract argumentation theory with an extended argumentation theory, and is thus based on a combination of the methodology of instantiating abstract arguments, and the methodology of extending Dung's basic argumentation frameworks with other relations among abstract arguments. The technique of meta-argumentation applies Dung's theory of…Read more
  •  24
    A general filtration method for modal logics
    Journal of Philosophical Logic 1 (1). 1972.
  •  9
    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
  •  51
    Resource-origins of Nonmonotonicity
    with John Woods
    Studia Logica 88 (1): 85-112. 2008.
    Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning from assumptions Δ to conclusions C without their being any deductive chain from Δ to C. Such jumps are done by various mechanisms which are strongly dependent on context and knowledge of how the actual world functions. Our aim is to motivate these jump rules as inference rules designed to optimise survival in an environment with scant resources of effort and time. We begin w…Read more
  •  3
    Defeasible inheritance systems and reactive diagrams
    Logic 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
  •  12
    General Intensional Logic
    with C. Anthony Anderson and F. Guenthner
    Journal of Symbolic Logic 55 (2): 892-894. 1990.
  •  1
    Handbook of Philosophical Logic Vol. 10 (edited book)
    with F. Guenther
    Kluwer Academic Publishers. 2003.
  •  22
    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
  •  16
    Alternative Set Theories
    with Thierry Libert, T. Forster, R. Holmes, John Woods, and Akihiro Kanamori
    In Dov Gabbay (ed.), The Handbook of the History of Logic, Elsevier. 2009.