Abstract
In this paper we introduce the polyadic tense \(\theta\)-valued \(\L\)ukasiewicz–Moisil algebras (=polyadic tense \(\hbox{LM}_{\theta}\)-algebras), as a common generalization of polyadic tense Boolean algebras and polyadic \(\hbox{LM}_{\theta}\)-algebras. Our main result is a representation theorem for polyadic tense \(\hbox{LM}_{\theta}\)-algebras.
Similar content being viewed by others
References
Boicescu V (1971) Sur les systèmes déductifs dans la logique θ-valente. Publ Dép Math Lyon 8:123–133
Boicescu V, Filipoiu A, Georgescu G, Rudeanu S (1991) \(\L\)ukasiewicz–Moisil algebras. North-Holland
Burgess JP (1984) Basic tense logic. In: Gabbay DM, Guenthner F (eds) Handbook of philosophical logic, vol II. D. Reidel, pp 89–133
Chiriţă C (2010) θ-Valued Moisil propositional logic. Int J Comput Commun Control 5(5):642–653. ISSN:1841-9836
Chiriţă C (2011) Tense θ-valued Łukasiewicz–Moisil algebras. J Multiple-Valued Logic Soft Comput 17(1):1–24
Filipoiu A (1981) \(\theta\)-Valued \(\L\)ukasiewicz–Moisil algebras and logics. PhD thesis, University of Bucharest
Georgescu G (1979) A representation theorem for polyadic tense algebras. Mathematica, Tome 21(44), No 2, pp 131–138
Georgescu G, Vraciu C (1970) On the characterization of centered \(\L\)ukasiewicz algebras. J Algebra 16:486–495
Goldblatt R (1992) Logics of time and computation. CSLI lecture notes no 7
Halmos PR (1962) Algebraic logic. Chelsea
Moisil GrC (1968) \(\L\)ukasiewiczian algebras. Computing Center, University of Bucharest, pp 311–324
Moisil GrC (1972) Essais sur les logiques non-chrysippiennes, Ed. Academiei, Bucharest
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chiriţă, C. Polyadic tense \(\theta\)-valued \(\L\)ukasiewicz–Moisil algebras. Soft Comput 16, 979–987 (2012). https://doi.org/10.1007/s00500-011-0796-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-011-0796-y