7 found
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  1.  4
    A Constructive Galois Connection Between Closure and Interior.Francesco Ciraulo & Giovanni Sambin - 2012 - Journal of Symbolic Logic 77 (4):1308-1324.
    We construct a Galois connection between closure and interior operators on a given set. All arguments are intuitionistically valid. Our construction is an intuitionistic version of the classical correspondence between closure and interior operators via complement.
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  2.  4
    A Constructive Semantics for Non-Deducibility.Francesco Ciraulo - 2008 - Mathematical Logic Quarterly 54 (1):35-48.
    This paper provides a constructive topological semantics for non-deducibility of a first order intuitionistic formula. Formal topology theory, in particular the recently introduced notion of a binary positivity predicate, and co-induction are two needful tools.
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  3.  26
    Regular Opens in Constructive Topology and a Representation Theorem for Overlap Algebras.Francesco Ciraulo - 2013 - Annals of Pure and Applied Logic 164 (4):421-436.
    Giovanni Sambin has recently introduced the notion of an overlap algebra in order to give a constructive counterpart to a complete Boolean algebra. We propose a new notion of regular open subset within the framework of intuitionistic, predicative topology and we use it to give a representation theorem for overlap algebras. In particular we show that there exists a duality between the category of set-based overlap algebras and a particular category of topologies in which all open subsets are regular.
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  4.  1
    Embedding Locales and Formal Topologies Into Positive Topologies.Francesco Ciraulo & Giovanni Sambin - forthcoming - Archive for Mathematical Logic:1-14.
    A positive topology is a set equipped with two particular relations between elements and subsets of that set: a convergent cover relation and a positivity relation. A set equipped with a convergent cover relation is a predicative counterpart of a locale, where the given set plays the role of a set of generators, typically a base, and the cover encodes the relations between generators. A positivity relation enriches the structure of a locale; among other things, it is a tool to (...)
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  5.  4
    Intuitionistic Overlap Structures.Francesco Ciraulo - 2013 - Logic and Logical Philosophy 22 (2):201-212.
    We study some connections between two kinds of emph{overlap} relations: that of point-free geometries in the sense of Grzegorczyk, Whitehead and Clarke, and that recently introduced by Sambin within his constructive approach to topology. The main thesis of this paper is that the overlap relation in the latter sense is a necessary tool for a constructive and intuitionistic development of point-free geometry.
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  6.  2
    Positivity Relations on a Locale.Francesco Ciraulo & Steven Vickers - 2016 - Annals of Pure and Applied Logic 167 (9):806-819.
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  7.  2
    A Constructive Investigation of Satisfiability.Francesco Ciraulo - 2012 - Annals of Pure and Applied Logic 163 (2):111-121.