•  65
    Context-dependent Abduction and Relevance
    with Rolf Nossum and John Woods
    Journal of Philosophical Logic 35 (1): 65-81. 2006.
    Based on the premise that what is relevant, consistent, or true may change from context to context, a formal framework of relevance and context is proposed in which • contexts are mathematical entities • each context has its own language with relevant implication • the languages of distinct contexts are connected by embeddings • inter-context deduction is supported by bridge rules • databases are sets of formulae tagged with deductive histories and the contexts they belong to • abduction and rev…Read more
  •  1
    Handbook of Philosophical Logic Vol. 10 (edited book)
    with F. Guenther
    Kluwer Academic Publishers. 2003.
  •  3
    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.
  •  14
    Non-Cooperation In Dialogue Logic
    with John Woods
    Synthese 127 (1): 161-186. 2001.
  •  18
    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
  •  9
    The attack as strong negation, part I
    with M. Gabbay
    Logic Journal of the IGPL 23 (6): 881-941. 2015.
  •  22
    Filtration structures and the cut down problem in abduction
    with John Woods
    In John Woods, Kent A. Peacock & A. D. Irvine (eds.), Mistakes of Reason: Essays in Honour of John Woods, University of Toronto Press. pp. 398-417. 2005.
  • Mathematical Problems from Applied Logic I
    with Sergei S. Goncharov and Michael Zakharyaschev
    Studia Logica 87 (2-3): 363-367. 2007.
  • What Is a Logical System?
    Studia Logica 61 (2): 302-304. 1998.
  •  140
    Advice on Abductive Logic
    with John Woods
    Logic Journal of the IGPL 14 (2): 189-219. 2006.
    One of our purposes here is to expose something of the elementary logical structure of abductive reasoning, and to do so in a way that helps orient theorists to the various tasks that a logic of abduction should concern itself with. We are mindful of criticisms that have been levelled against the very idea of a logic of abduction; so we think it prudent to proceed with a certain diffidence. That our own account of abduction is itself abductive is methodological expression of this diffidence. A s…Read more
  •  25
    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
  •  8
    Extensions of Classical Logic
    with Robert Bull, Krister Segerberg, and F. Guenthner
    Journal of Symbolic Logic 54 (4): 1472-1477. 1989.
  •  11
    Theory of disjunctive attacks, Part I
    with M. Gabbay
    Logic Journal of the IGPL 24 (2): 186-218. 2016.
  •  6
    A General Theory of Structured Consequence Relations
    Theoria: 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
  • Sets and extensions in the twentieth century
    with Akihiro Kanamori and John Woods
    In Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.), Handbook of the History of Logic, Elsevier. 2004.
  •  7
    Handbook of Philosophical Logic, Volume II. Extensions of Classical Logic
    with J. K. Slaney and Franz Guenther
    Philosophical Quarterly 36 (142): 101. 1986.
  • Editorial
    Logic Journal of the IGPL 6 (1): 1-1. 1998.
  •  68
    Sequential Dynamic Logic
    with Alexander Bochman
    Journal of Logic, Language and Information 21 (3): 279-298. 2012.
    We introduce a substructural propositional calculus of Sequential Dynamic Logic that subsumes a propositional part of dynamic predicate logic, and is shown to be expressively equivalent to propositional dynamic logic. Completeness of the calculus with respect to the intended relational semantics is established.
  •  123
    Handbook of the History of Logic (edited book)
    with John Woods and Akihiro Kanamori
    Elsevier. 2004.
    Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Gödel, The Emergence of Classical Logic, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, includ…Read more
  •  10
    Forthcoming Papers
    with Y. Shramko, J. Barwise, and J. van Benthem
    Logic Journal of the Igpl 3 (5): 815-816. 1995.
  •  30
    Reactive intuitionistic tableaux
    Synthese 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
  • J. EL1ASSON Ultrapowers as sheaves on a category of ultrafilters 825 A. LEWIS Finite cupping sets 845
    with G. Metcalfe, N. Olivetti, H. Towsner, M. Dzamonja, and S. Shelah
    Archive for Mathematical Logic 43 (7): 934. 2004.
  •  9
    Cumulativity without closure of the domain under finite unions
    with Karl Schlechta
    Review of Symbolic Logic 1 (3): 372-392. 2008.
    For nonmonotonic logics, Cumulativity is an important logical rule. We show here that Cumulativity fans out into an infinity of different conditions, if the domain is not closed under finite unions
  • Handbook of Logic in Computer Science
    with Samson Abramsky and Thomas S. E. Maibaum
    . 1992.
  •  25
    On modal logics characterized by models with relative accessibility relations: Part II
    with Stéphane Demri
    Studia Logica 66 (3): 349-384. 2000.
    This work is divided in two papers (Part I and Part II). In Part I, we introduced 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 were established by faithfully translating the Rare-logics into more standard modal logics (some of th…Read more
  •  40
    Preface for Studia Logica Special Issue (2)
    with Dov M. Gabbay and Leendert van der Torre
    Studia Logica 93 (2-3). 2009.