Hyperboolean Algebras and Hyperboolean Modal Logic
Journal of Applied Non-Classical Logics 9 (2):345-368 (1999)
Abstract
Hyperboolean algebras are Boolean algebras with operators,
constructed as algebras of complexes (or, power structures) of Boolean
algebras. They provide an algebraic semantics for a modal logic
(called here a {\em hyperboolean modal logic}) with a Kripke semantics
accordingly based on frames in which the worlds are elements of
Boolean algebras and the relations correspond to the Boolean
operations. We introduce the hyperboolean modal logic, give a
complete axiomatization of it, and show that it lacks the finite model
property. The method of axiomatization hinges upon the fact that a
"difference" operator is definable in hyperboolean algebras, and makes
use of additional non-Hilbert-style rules. Finally, we discuss a
number of open questions and directions for further research.
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Archival date: 2018-04-21
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2013-12-01
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Recent downloads (6 months)
13 ( #50,087 of 70,272 )
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