Discrete Duality for Tense Łukasiewicz-Moisil Algebras

In 2007, tense Łukasiewicz–Moisil algebras were introduced by Diaconescu and Georgescu as an algebraic counterpart of tense n–valued Moisil logic. These algebras constitute a generalization of tense algebras. In this paper we describe a discrete duality for tense Łukasiewicz–Moisil algebras bearing in mind the results indicated by Dzik, Orlowska and van Alten in 2006, for De Morgan algebras.

[1]  Carmen Chirita.  Polyadic tense h-valued èukasiewicz-Moisil algebras , 2012 .

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

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

[4]  Carmen Chirita.  Polyadic tense $$\theta$$-valued $$\L$$ukasiewicz–Moisil algebras , 2012, Soft Comput..

[5]  Jan Paseka,et al.  Operators on MV-algebras and their representations , 2013, Fuzzy Sets Syst..

[6]  DiaconescuDenisa,et al.  Tense Operators on MV-Algebras and ukasiewicz-Moisil Algebras , 2007 .

[7]  Ewa Orlowska,et al.  Discrete Duality and Its Applications to Reasoning with Incomplete Information , 2007, RSEISP.

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

[9]  Ivan Chajda,et al.  Dynamic effect algebras , 2012 .

[10]  Aldo V. Figallo,et al.  Tense operators on De Morgan algebras , 2014, Log. J. IGPL.

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

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

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

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

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

[16]  Jan Paseka,et al.  Dynamic effect algebras and their representations , 2012, Soft Comput..

[17]  A. Tarski,et al.  Boolean Algebras with Operators , 1952 .

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

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

[20]  Ewa Orlowska,et al.  Duality via Truth: Semantic frameworks for lattice-based logics , 2005, Log. J. IGPL.

[21]  George Georgescu,et al.  Lukasiewicz-Moisil algebras , 2012, Annals of discrete mathematics.

[22]  Albert A. Bennett.  Review: Gr. C. Moisil, Recherches sur les Logiques Non-Chrysippiennes , 1948 .