Artículo
Abstract:
In this paper we introduce two kinds of unary operations on abelian ℓ-groups with a positive distinguished element u. One of them, called demiquantifier of type I, behaves like an existential quantifier (in the sense of Cimadamore and Varela) in the negative cone, and like a universal quantifier in the positive cone. The other kind of unary operation we introduce, called demiquantifier of type II, satisfies analogous properties to demiquantifiers of type I via a translation of the negative cone, by means of the element u. These unary operations are interdefinable with the usual existential quantifiers, provided the distinguished element u is a strong unit. Moreover, if G is an abelian ℓ-group, then the restriction of a demiquantifier of type II to the MV-algebra Γ (G, u) yields a different type of quantifier, where Γ is Mundici’s functor. These quantifiers are interdefinable with the usual existential quantifiers on MV-algebras given by Rutledge, provided that the involution of the corresponding MV-algebras have a fixed point. © 2018, Springer Nature Switzerland AG.
Registro:
| Documento: | Artículo |
| Título: | Demiquantifiers on ℓ -groups |
| Autor: | Petrovich, A. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, Argentina Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de La Pampa, Uruguay 151, Santa Rosa, La Pampa, Argentina |
| Palabras clave: | MV-algebras; Quantifiers; ℓ-groups |
| Año: | 2018 |
| Volumen: | 79 |
| Número: | 3 |
| DOI: | http://dx.doi.org/10.1007/s00012-018-0552-6 |
| Título revista: | Algebra Universalis |
| Título revista abreviado: | Algebra Univers. |
| ISSN: | 00025240 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00025240_v79_n3_p_Petrovich |
Referencias:
- Belluce, L.P., Grigolia, R., Lettieri, A., Representations of Monadic MValgebras (2005) Studia Logica, 81 (1), pp. 123-144
- Bigard, A., Keimel, K., Wolfenstein, S., (1977) Groupes et anneaux reticules, 608. , Lecture Notes Mathematics, Springer, Verlag
- Cimadamore, C., Diaz Varela, P., Monadic MV-algebras, are equivalent to Monadic ℓ -groups (2011) Studia Logica, 98, pp. 175-201. , Special Issue
- Cignoli, R., D’Ottaviano, I., Mundici, D., (2000) Algebraic Foundations of Many-Valued Reasoning, , Trends Logic. Springer, New York
- Di Nola, A., Grigolia, R., On monadic MV-algebras (2004) Ann. Pure Appl. Logic, 128 (1-3), pp. 125-139
- Lattanzi, M., Petrovich, A., An alternative notion of quantifiers on three-valued Łukasiewicz algebras (2017) J. Multiple Valued Logic Soft Comput., 28 (4-5), pp. 335-360
- Mundici, D., Interpretation of FA C* algebras in Łukasiewicz Sentential Calculus (1986) J. Funct. Anal., 65 (1), pp. 15-63
- Rutledge, J.D., (1959) A Preliminary Investigation of the Infinitely Many-Valued Predicate Calculus, , Ph. D. Thesis, Cornell University
Citas:
---------- APA ----------
(2018) . Demiquantifiers on ℓ -groups. Algebra Universalis, 79(3).http://dx.doi.org/10.1007/s00012-018-0552-6
---------- CHICAGO ----------
Petrovich, A. "Demiquantifiers on ℓ -groups" . Algebra Universalis 79, no. 3 (2018).http://dx.doi.org/10.1007/s00012-018-0552-6
---------- MLA ----------
Petrovich, A. "Demiquantifiers on ℓ -groups" . Algebra Universalis, vol. 79, no. 3, 2018.http://dx.doi.org/10.1007/s00012-018-0552-6
---------- VANCOUVER ----------
Petrovich, A. Demiquantifiers on ℓ -groups. Algebra Univers. 2018;79(3).http://dx.doi.org/10.1007/s00012-018-0552-6
