Abstract
We introduce relativized modal algebra homomorphisms and show that the category of modal algebras and relativized modal algebra homomorphisms is dually equivalent to the category of modal spaces and partial continuous p-morphisms, thus extending the standard duality between the category of modal algebras and modal algebra homomorphisms and the category of modal spaces and continuous p-morphisms. In the transitive case, this yields an algebraic characterization of Zakharyaschev’s subreductions, cofinal subreductions, dense subreductions, and the closed domain condition. As a consequence, we give an algebraic description of canonical, subframe, and cofinal subframe formulas, and provide a new algebraic proof of Zakharyaschev’s theorem that each logic over K4 is axiomatizable by canonical formulas.
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Dedicated to Ryszard Wójcicki on his 80th birthday
Special issue in honor of Ryszard Wójcicki on the occasion of his 80th birthday
Edited by J. Czelakowski, W. Dziobiak, and J. Malinowski
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Bezhanishvili, G., Bezhanishvili, N. An Algebraic Approach to Canonical Formulas: Modal Case. Stud Logica 99, 93 (2011). https://doi.org/10.1007/s11225-011-9348-9
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DOI: https://doi.org/10.1007/s11225-011-9348-9