25 found
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  1.  66
    Standard Gödel Modal Logics.Xavier Caicedo & Ricardo O. Rodriguez - 2010 - Studia Logica 94 (2):189-214.
    We prove strong completeness of the □-version and the ◊-version of a Gödel modal logic based on Kripke models where propositions at each world and the accessibility relation are both infinitely valued in the standard Gödel algebra [0,1]. Some asymmetries are revealed: validity in the first logic is reducible to the class of frames having two-valued accessibility relation and this logic does not enjoy the finite model property, while validity in the second logic requires truly fuzzy accessibility relations and this (...)
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  2.  5
    Equivalence and Quantifier Rules for Logic with Imperfect Information.Xavier Caicedo, Francien Dechesne & Theo Janssen - 2008 - Logic Journal of the IGPL 17 (1):91-129.
    In this paper, we present a prenex form theorem for a version of Independence Friendly logic, a logic with imperfect information. Lifting classical results to such logics turns out not to be straightforward, because independence conditions make the formulas sensitive to signalling phenomena. In particular, nested quantification over the same variable is shown to cause problems. For instance, renaming of bound variables may change the interpretations of a formula, there are only restricted quantifier extraction theorems, and slashed connectives cannot be (...)
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  3.  7
    Omitting Uncountable Types and the Strength of [0,1]-Valued Logics.Xavier Caicedo & José N. Iovino - 2014 - Annals of Pure and Applied Logic 165 (6):1169-1200.
    We study a class of [0,1][0,1]-valued logics. The main result of the paper is a maximality theorem that characterizes these logics in terms of a model-theoretic property, namely, an extension of the omitting types theorem to uncountable languages.
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  4.  58
    An Algebraic Approach to Intuitionistic Connectives.Xavier Caicedo & Roberto Cignoli - 2001 - Journal of Symbolic Logic 66 (4):1620-1636.
    It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting (...)
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  5.  41
    Implicit Connectives of Algebraizable Logics.Xavier Caicedo - 2004 - Studia Logica 78 (1-2):155 - 170.
    An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, all (...)
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  6.  6
    Implicit Connectives of Algebraizable Logics.Xavier Caicedo - 2004 - Studia Logica 78 (1):155-170.
    An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, all (...)
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  7.  4
    A Formal System for the Non-Theorems of the Propositional Calculus.Xavier Caicedo - 1978 - Notre Dame Journal of Formal Logic 19:147.
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  8.  24
    Lindström’s Theorem for Positive Logics, a Topological View. [REVIEW]Xavier Caicedo - 2015 - In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. pp. 73-90.
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  9.  10
    Compactness and Normality in Abstract Logics.Xavier Caicedo - 1993 - Annals of Pure and Applied Logic 59 (1):33-43.
    We generalize a theorem of Mundici relating compactness of a regular logic L to a strong form of normality of the associated spaces of models. Moreover, it is shown that compactness is in fact equivalent to ordinary normality of the model spaces when L has uniform reduction for infinite disjoint sums of structures. Some applications follow. For example, a countably generated logic is countably compact if and only if every clopen class in the model spaces is elementary. The model spaces (...)
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  10. A Simple Solution to Friedman's Fourth Problem.Xavier Caicedo - 1986 - Journal of Symbolic Logic 51 (3):778-784.
    It is shown that Friedman's problem, whether there exists a proper extension of first order logic satisfying the compactness and interpolation theorems, has extremely simple positive solutions if one considers extensions by generalized (finitary) propositional connectives. This does not solve, however, the problem of whether such extensions exist which are also closed under relativization of formulas.
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  11.  18
    Hilbert∈-Symbol in the Presence of Generalized Quantifiers.Xavier Caicedo - 1991 - Bulletin of the Section of Logic 20 (3/4):85-86.
  12.  18
    Continuous Operations on Spaces of Structures.Xavier Caicedo - 1995 - In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. pp. 263--296.
  13.  9
    An Algebraic Approach to Intuitionistic Connectives.Xavier Caicedo & Roberto Cignoli - 2001 - Journal of Symbolic Logic 66 (4):1620-1636.
    It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting (...)
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  14.  3
    Completud de dos cálculos logicos de Leibniz.Xavier Caicedo & Alejandro Martín - 2001 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 16 (3):539-558.
    Este trabajo se encuadra dentro de una nueva visión de la lógica de Leibniz, la cual pretende mostrar que sus escritos fueron ricos no solamente en proyectos ambiciosos sino también en desarrollos lógico-matematicos concretos. Se demuestra que su “Caracteristica Numerica” que asigna pares de números a las proposiciones categóricas es una semántiea para la cual la silogística aristotélica es correcta y completa, y que el sistema algebraico presentado en Fundamentos de un Cálculo Lógico es una lógica algebraica similar a la (...)
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  15.  5
    On Extensions of $L{\Omega \Omega }(Q1)$.Xavier Caicedo - 1981 - Notre Dame Journal of Formal Logic 22 (1):85-93.
  16. Meeting of the Association for Symbolic Logic: Bogotá, Colombia, 1981.Ayda I. Arruda, Xavier Caicedo, Rolando Chuaqui & Newton C. A. Costa - 1983 - Journal of Symbolic Logic 48 (3):884-892.
  17.  35
    Meeting of the Association for Symbolic Logic: Bogotá, Colombia, 1981.Ayda I. Arruda, Xavier Caicedo, Rolando Chuaqui & Newton C. A. da Costa - 1983 - Journal of Symbolic Logic 48 (3):884 - 892.
  18.  16
    Definability and Automorphisms in Abstract Logics.Xavier Caicedo - 2004 - Archive for Mathematical Logic 43 (8):937-945.
    In any model theoretic logic, Beth’s definability property together with Feferman-Vaught’s uniform reduction property for pairs imply recursive compactness, and the existence of models with infinitely many automorphisms for sentences having infinite models. The stronger Craig’s interpolation property plus the uniform reduction property for pairs yield a recursive version of Ehrenfeucht-Mostowski’s theorem. Adding compactness, we obtain the full version of this theorem. Various combinations of definability and uniform reduction relative to other logics yield corresponding results on the existence of non-rigid (...)
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  19.  25
    Definability Properties and the Congruence Closure.Xavier Caicedo - 1990 - Archive for Mathematical Logic 30 (4):231-240.
    We introduce a natural class of quantifiersTh containing all monadic type quantifiers, all quantifiers for linear orders, quantifiers for isomorphism, Ramsey type quantifiers, and plenty more, showing that no sublogic ofL ωω (Th) or countably compact regular sublogic ofL ∞ω (Th), properly extendingL ωω , satisfies the uniform reduction property for quotients. As a consequence, none of these logics satisfies eitherΔ-interpolation or Beth's definability theorem when closed under relativizations. We also show the failure of both properties for any sublogic ofL (...)
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  20.  16
    Hilbert's Ε-Symbol in the Presence of Generalized Quantifiers.Xavier Caicedo - 1995 - In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. pp. 63--78.
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  21. Models, Algebras, and Proofs Selected Papers of the X Latin American Symposium on Mathematical Logic Held in Bogotá.Xavier Caicedo & Carlos H. Montenegro - 1999
     
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  22.  11
    Meeting of the Assocaition for Symbolic Logic: Caracas, Venezuela, 1983.Xavier Caicedo, Rolando Chauqui, Newton C. D. da Costa & Carlos A. Di Prisco - 1984 - Journal of Symbolic Logic 49 (4):1430 - 1440.
  23.  8
    Meeting of the Association for Symbolic Logic.Xavier Caicedo, Rolando Chuaqui, Newton C. A. Da Costa & Carlos A. Di Prisco - 1984 - Journal of Symbolic Logic 49 (4):1430-1440.
  24.  21
    Meeting of the Assocaition for Symbolic Logic: Caracas, Venezuela, 1983.Xavier Caicedo - 1984 - Journal of Symbolic Logic 49 (4):1430-1440.
  25.  11
    25th Workshop on Logic, Language, Information and Computation.Lawrence Moss, Maricarmen Martinez, Xavier Caicedo & Ruy de Queiroz - 2019 - Logic Journal of the IGPL 27 (5):766-776.
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