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Vol. 13(2) 2013
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Vol. 13(3), 2013
On the relationship between tetravalent modal algebras, symmetric Boolean algebras and modal algebras for S5
Marcelo E. Coniglio (1); Martín Figallo (2)

(1) CLE and Department of Philosophy
State University of Campinas
Campinas, Brazil

(2) Departamento de Matemática
Universidad Nacional del Sur
Bahía Blanca, Argentina


Update: the final version of this paper has been  published as: M.E. Coniglio; M. Figallo. On a four-valued modal logic with deductive implication. Bulletin of the Section of Logic 43, n. 1/2: 1-18, 2014.

Date Posted: April 29, 2013

vol. 13, n. 3, 2013

   
Abstract:

In this paper we prove, on the one hand, that A. Monteiro's tetravalent modal algebras plus a Boolean complement are the same as De Morgan algebras plus a Boolean complement or, equivalently, Boolean algebras plus a De Morgan negation. The latter are called symmetric
(or involutive) Boolean algebras (IBAs), introduced by Gr. Moisil and mainly studied by A. Monteiro. On the other hand, we prove that IBAs are modal algebras for modal logic S5 satisfying additional equations such that the variety of IBAs is generated by the Henle algebra H2. Thus, the logic that can be naturally associated to IBAs is a proper
normal extension of S5.


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