1.  74
    Formal systems for modal operators on locales.Gonzalo E. Reyes & Marek W. Zawadowski - 1993 - Studia Logica 52 (4):595 - 613.
    In the paper [8], the first author developped a topos- theoretic approach to reference and modality. (See also [5]). This approach leads naturally to modal operators on locales (or spaces without points). The aim of this paper is to develop the theory of such modal operators in the context of the theory of locales, to axiomatize the propositional modal logics arising in this context and to study completeness and decidability of the resulting systems.
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  2.  18
    Descent and duality.Marek W. Zawadowski - 1995 - Annals of Pure and Applied Logic 71 (2):131-188.
    Using the Makkai's duality for first-order logic, we characterise effective descent morphisms in 2-categories of pretoposes and Barr-exact categories. In both cases they coincide with conservative morphisms. We show that in those 2-categories the 2-coregular factorisations are exactly quotient-conservative factorisations. We also prove a generalisation of the Makkai duality for pseudoelementary categories.
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  3.  21
    Pre-Ordered Quantifiers in Elementary Sentences of Natural Language.Marek W. Zawadowski - 1995 - In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. pp. 237--253.
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