Tense operators on De Morgan algebras

The purpose of this article is to investigate the variety of algebras, which we call tense De Morgan algebras, as a natural generalization of tense algebras developed in Burges (1984, Handbook of Philosophical Logic, vol. II, pp. 89–139) (see also, Kowalski (1998, Rep. Math. Logic, 32, 53–95)). It is worth mentioning that the latter is a proper subvariety of the first one, as it is shown in a simple example. Our main interest is the representation theory for these classes of algebras.

[1]  Hilary A. Priestley,et al.  Ordered Topological Spaces and the Representation of Distributive Lattices , 1972 .

[2]  Carmen Chiriţă.  Tense θ-valued Moisil propositional logic , 2010, Int. J. Comput. Commun. Control.

[3]  H. Priestley,et al.  Distributive Lattices , 2004 .

[4]  Aldo V. Figallo,et al.  DISCRETE DUALITY FOR TSH-ALGEBRAS , 2012 .

[5]  Ivan Chajda,et al.  Tense Operators on Basic Algebras , 2011 .

[6]  Hilary A. Priestley,et al.  Ordered Sets and Duality for Distributive Lattices , 1984 .

[7]  George Georgescu,et al.  Tense Operators on MV-Algebras and Lukasiewicz-Moisil Algebras , 2007, Fundam. Informaticae.

[8]  William H. Cornish,et al.  Coproducts of De Morgan algebras , 1977, Bulletin of the Australian Mathematical Society.

[9]  Aldo V. Figallo,et al.  Remarks on Heyting algebras with tense operators , 2012 .

[10]  Helena Rasiowa,et al.  On the Representation of Quasi-Boolean Algebras , 1957 .

[11]  J. A. Kalman,et al.  Lattices with involution , 1958 .

[12]  Carmen Chirita.  Tense -0-Valued Lukasiewicz-Moisil Algebras , 2011, J. Multiple Valued Log. Soft Comput..

[13]  A. Figallo,et al.  Tense Operators on m-Symmetric Algebras , 2012, 1203.5374.

[14]  Tomasz Kowalski,et al.  Varieties of Tense Algebras , 1998, Reports Math. Log..

[15]  Aldo V. Figallo,et al.  Note on tense SHn-algebras , 2011 .

[16]  Nuel D. Belnap,et al.  A Useful Four-Valued Logic , 1977 .

[17]  John P. Burgess,et al.  Basic Tense Logic , 1984 .

[18]  Ewa Orlowska,et al.  Relational Representation Theorems for General Lattices with Negations , 2006, RelMiCS.

[19]  Ivan Chajda,et al.  Algebraic axiomatization of tense intuitionistic logic , 2011 .

[20]  Hilary A. Priestley,et al.  Representation of Distributive Lattices by means of ordered Stone Spaces , 1970 .