Hyperboolean Algebras and Hyperboolean Modal Logic
作者:
Valentin Goranko,
Dimiter Vakarelov,
期刊:
Journal of Applied Non-Classical Logics
(Taylor Available online 1999)
卷期:
Volume 9,
issue 2-3
页码: 345-368
ISSN:1166-3081
年代: 1999
DOI:10.1080/11663081.1999.10510971
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
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 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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