Modal operators on bounded commutative residuated ℓ -monoids

by: Jiří Rachůnek, Dana Šalounová

Mathematica Slovaca, Vol. 57, No. 4. (2007), pp. 321-332.

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Abstract

Abstract Bounded commutative residuated lattice ordered monoids (Rℓ-monoids) are a common generalization of, e.g., Heyting algebras and BL-algebras, i.e., algebras of intuitionistic logic and basic fuzzy logic, respectively. Modal operators (special cases of closure operators) on Heyting algebras were studied in [MacNAB, D. S.: Modal operators on Heyting algebras, Algebra Universalis 12 (1981), 5–29] and on MV-algebras in [HARLENDEROV�,M.—RACHŮNEK, J.: Modal operators on MV-algebras, Math. Bohem. 131 (2006), 39–48]. In the paper we generalize the notion of a modal operator for general bounded commutative Rℓ-monoids and investigate their properties also for certain derived algebras.

@article{citeulike:2140993, abstract = {Abstract\ \ Bounded commutative residuated lattice ordered monoids (Rℓ-monoids) are a common generalization of, e.g., Heyting algebras and BL-algebras, i.e., algebras of intuitionistic logic and basic fuzzy logic, respectively. Modal operators (special cases of closure operators) on Heyting algebras were studied in [MacNAB, D. S.: Modal operators on Heyting algebras, Algebra Universalis 12 (1981), 5–29] and on MV-algebras in [HARLENDEROV�,M.—RACH\r{U}NEK, J.: Modal operators on MV-algebras, Math. Bohem. 131 (2006), 39–48]. In the paper we generalize the notion of a modal operator for general bounded commutative Rℓ-monoids and investigate their properties also for certain derived algebras.}, author = {Rach\r{u}nek, Ji\v{r}\'{i} and \v{S}alounov\'{a}, Dana }, citeulike-article-id = {2140993}, doi = {http://dx.doi.org/10.2478/s12175-007-0026-3}, journal = {Mathematica Slovaca}, keywords = {\_copy, \_file, closure\_operator, modal\_operator, mv-algebra, nucleus, residuation}, number = {4}, pages = {321--332}, posted-at = {2007-12-18 13:34:28}, priority = {2}, title = {Modal operators on bounded commutative residuated ℓ -monoids}, url = {http://dx.doi.org/10.2478/s12175-007-0026-3}, volume = {57}, year = {2007} }

RIS record

TY - JOUR ID - citeulike:2140993 L3 - citeulike-article-id:2140993 TI - Modal operators on bounded commutative residuated ℓ -monoids JF - Mathematica Slovaca VL - 57 IS - 4 SP - 321 EP - 332 N2 - Abstract  Bounded commutative residuated lattice ordered monoids (Rℓ-monoids) are a common generalization of, e.g., Heyting algebras and BL-algebras, i.e., algebras of intuitionistic logic and basic fuzzy logic, respectively. Modal operators (special cases of closure operators) on Heyting algebras were studied in [MacNAB, D. S.: Modal operators on Heyting algebras, Algebra Universalis 12 (1981), 5–29] and on MV-algebras in [HARLENDEROV�,M.—RACHŮNEK, J.: Modal operators on MV-algebras, Math. Bohem. 131 (2006), 39–48]. In the paper we generalize the notion of a modal operator for general bounded commutative Rℓ-monoids and investigate their properties also for certain derived algebras. KW - _copy KW - _file KW - closure_operator KW - modal_operator KW - mv-algebra KW - nucleus KW - residuation AU - Rachůnek, Jiří AU - Šalounová, Dana PY - 2007//26/ UR - http://dx.doi.org/10.2478/s12175-007-0026-3 ER -

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