
65Contextdependent Abduction and RelevanceJournal of Philosophical Logic 35 (1): 6581. 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 • intercontext 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

3Journal of Applied Logic Special Volume on NeuralSymbolic SystemsJournal of Applied Logic 2 (3): 241243. 2004.

18A Sound And Complete Deductive System For Ctl* VerificationLogic Journal of the IGPL 16 (6): 499536. 2008.The paper presents a compositional approach to the verification of CTL* properties over reactive systems. Both symbolic modelchecking 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

22Filtration structures and the cut down problem in abductionIn John Woods, Kent A. Peacock & A. D. Irvine (eds.), Mistakes of Reason: Essays in Honour of John Woods, University of Toronto Press. pp. 398417. 2005.

140Advice on Abductive LogicLogic Journal of the IGPL 14 (2): 189219. 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

25Semantic interpolationJournal of Applied NonClassical Logics 20 (4): 345371. 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". Nonmonotonic logics like preferential logics are often a mixture of a nonmonotonic 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

4Extending the CurryHoward Interpretation to Linear, Relevant and Other Resource LogicsJournal of Symbolic Logic 57 (4). 1992.

11Kripke Saul A.. Semantical considerations for modal logics. Proceedings of a Colloquium on Modal and Manyvalued Logics, Helsinki, 2326 August, 1962, Acta Philosophica Fennica 1963, pp. 83–94 (review)Journal of Symbolic Logic 34 (3): 501501. 1969.

6A General Theory of Structured Consequence RelationsTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 10 (2): 4978. 1995.There are several areas in logic where the monotonicity of the consequence relation fails to hold. Roughly these are the traditional nonmonotonic systems arising in Artificial Intelligence, numerical nonmonotonic 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 centuryIn Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.), Handbook of the History of Logic, Elsevier. 2004.

7Handbook of Philosophical Logic, Volume II. Extensions of Classical LogicPhilosophical Quarterly 36 (142): 101. 1986.

68Sequential Dynamic LogicJournal of Logic, Language and Information 21 (3): 279298. 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.

123Handbook of the History of Logic (edited book)Elsevier. 2004.Greek, Indian and Arabic Logic marks the initial appearance of the multivolume 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 ManyValued and NonMonotonic Turn in Logic. Further volumes will follow, includ…Read more

28The decision problem for some finite extensions of the intuitionistic theory of abelian groupsStudia Logica 34 (1): 5967. 1975.

10

30Reactive intuitionistic tableauxSynthese 179 (2): 253269. 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 845Archive for Mathematical Logic 43 (7): 934. 2004.

9Cumulativity without closure of the domain under finite unionsReview of Symbolic Logic 1 (3): 372392. 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

25On modal logics characterized by models with relative accessibility relations: Part IIStudia Logica 66 (3): 349384. 2000.This work is divided in two papers (Part I and Part II). In Part I, we introduced the class of Rarelogics 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 Rarelogics, reductions for decidability were established by faithfully translating the Rarelogics into more standard modal logics (some of th…Read more