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  1. Leo Esakia on Duality in Modal and Intuitionistic Logics.Guram Bezhanishvili (ed.) - 2014 - Dordrecht, Netherland: Springer.
    This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia’s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area. Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations (...)
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  • Independence-friendly cylindric set algebras.Allen Mann - 2009 - Logic Journal of the IGPL 17 (6):719-754.
    Independence-friendly logic is a conservative extension of first-order logic that has the same expressive power as existential second-order logic. We attempt to algebraize IF logic in the same spirit as cylindric algebra. We define independence-friendly cylindric set algebras and investigate to what extent they satisfy the axioms of cylindric algebra. We ask whether the equational theory of IF algebras is finitely axiomatizable, and prove two partial results. First, every IF algebra over a structure is an expansion of a Kleene algebra. (...)
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  • Distributive Lattices with a Negation Operator.Sergio Arturo Celani - 1999 - Mathematical Logic Quarterly 45 (2):207-218.
    In this note we introduce and study algebras of type such that is a bounded distributive lattice and ⌝ is an operator that satisfies the condition ⌝ = a ⌝ b and ⌝ 0 = 1. We develop the topological duality between these algebras and Priestley spaces with a relation. In addition, we characterize the congruences and the subalgebras of such an algebra. As an application, we will determine the Priestley spaces of quasi-Stone algebras.
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  • Bounded distributive lattices with strict implication.Sergio Celani & Ramon Jansana - 2005 - Mathematical Logic Quarterly 51 (3):219-246.
    The present paper introduces and studies the variety WH of weakly Heyting algebras. It corresponds to the strict implication fragment of the normal modal logic K which is also known as the subintuitionistic local consequence of the class of all Kripke models. The tools developed in the paper can be applied to the study of the subvarieties of WH; among them are the varieties determined by the strict implication fragments of normal modal logics as well as varieties that do not (...)
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