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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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