Hyperboolean Algebras and Hyperboolean Modal Logic

Journal of Applied Non-Classical Logics 9 (2):345-368 (1999)
  Copy   BIBTEX

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.

Author Profiles

Analytics

Added to PP
2013-12-01

Downloads
314 (#56,138)

6 months
108 (#43,687)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?