6 found
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Maarten de Rijke [5]Maarten Rijke [4]
  1.  21
    Sahlqvist's Theorem for Boolean Algebras with Operators with an Application to Cylindric Algebras.Maarten De Rijke & Yde Venema - 1995 - Studia Logica 54 (1):61 - 78.
    For an arbitrary similarity type of Boolean Algebras with Operators we define a class of Sahlqvist identities. Sahlqvist identities have two important properties. First, a Sahlqvist identity is valid in a complex algebra if and only if the underlying relational atom structure satisfies a first-order condition which can be effectively read off from the syntactic form of the identity. Second, and as a consequence of the first property, Sahlqvist identities are canonical, that is, their validity is preserved under taking canonical (...)
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  2.  22
    Generalized Quantifiers and Modal Logic.Wiebe Hoek & Maarten Rijke - 1993 - Journal of Logic, Language and Information 2 (1):19-58.
    We study several modal languages in which some (sets of) generalized quantifiers can be represented; the main language we consider is suitable for defining any first order definable quantifier, but we also consider a sublanguage thereof, as well as a language for dealing with the modal counterparts of some higher order quantifiers. These languages are studied both from a modal logic perspective and from a quantifier perspective. Thus the issues addressed include normal forms, expressive power, completeness both of modal systems (...)
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  3.  22
    The Logic of Peirce Algebras.Maarten Rijke - 1995 - Journal of Logic, Language and Information 4 (3):227-250.
    Peirce algebras combine sets, relations and various operations linking the two in a unifying setting. This paper offers a modal perspective on Peirce algebras. Using modal logic as a characterization of the full Peirce algebras is given, as well as a finite axiomatization of their equational theory that uses so-called unorthodox derivation rules. In addition, the expressive power of Peirce algebras is analyzed through their connection with first-order logic and the fragment of first-order logic corresponding to Peirce algebras is described (...)
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  4.  31
    Jon Barwise and Jerry Seligman. Information Flow. The Logic of Distributed Systems. Cambridge Tracts in Theoretical Computer Science, No. 44. Cambridge University Press, Cambridge, New York, and Oakleigh, Victoria, 1997, Xv + 274 Pp. [REVIEW]Maarten De Rijke - 1999 - Journal of Symbolic Logic 64 (4):1836-1836.
  5.  39
    A Note on the Interpretability Logic of Finitely Axiomatized Theories.Maarten Rijke - 1991 - Studia Logica 50 (2):241 - 250.
    In [6] Albert Visser shows that ILP completely axiomatizes all schemata about provability and relative interpretability that are provable in finitely axiomatized theories. In this paper we introduce a system called ILP that completely axiomatizes the arithmetically valid principles of provability in and interpretability over such theories. To prove the arithmetical completeness of ILP we use a suitable kind of tail models; as a byproduct we obtain a somewhat modified proof of Visser's completeness result.
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  6.  1
    Special Issue on Combining Logics - Editor's Introduction.Patrick Blackburn & Maarten de Rijke - 1996 - Notre Dame Journal of Formal Logic 37 (2):161-166.