Boolean representation of bounded BCK-algebras

Soft Computing

Volumn 12, Issue 10, 2008, Pages 941-954

  Gispert, Joan ^a   Torrens, Antoni ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

Author keywords

Boolean factor elements; Bounded BCK algebras; Pierce BCK representation; Weak Boolean product

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATION THEORY; MATHEMATICAL MODELS; NUMERICAL METHODS;

BOOLEAN FACTOR ELEMENTS; BOUNDED BCK-ALGEBRAS; PIERCE BBCK-REPRESENTATION; WEAK BOOLEAN PRODUCT;

BOOLEAN ALGEBRA;

EID: 44349143909     PISSN: 14327643     EISSN: 14337479     Source Type: Journal    
DOI: 10.1007/s00500-007-0261-0     Document Type: Article

References (33)

1. Bigelow D and Burris S (1990). Boolean algebras of factor congruences. Acta Sci Math 54: 11-20
2. Blok WJ, Pigozzi D (1989) Algebraizable logics. Mem Am Math Soc 77(396) vii + 78 pp
3. Blok W and Raftery JG (1995). On the quasivariety of BCK-algebras and its subvarieties. Algebra Universalis 33: 68-90
4. Brown DJ and Suszko R (1973). Abstract logics. Diss Math 102: 4-42
5. Burris S and Sankappanavar HP (1981). A course in Universal algebra. Graduate text in Math, vol 78. Springer, New York
6. Burris S and Werner H (1979). Sheaf constructions and their elementary properties. Trans Am Math Soc 248: 269-309
7. Busaniche M (2003). Free algebras in varieties of BL-algebras generated by a chain. Algebra Universalis 50(3-4): 259-277
8. n-chain. J Aust Math Soc 80(3): 419-439
9. Cignoli R and Torrens A (1996). Boolean products of MV-algebras: hypernormal MV-algebras. J Math Anal Appl 99: 637-653
10. Cignoli R and Torrens A (2002). Free algebras in varieties of BL-algebras with a Boolean retract. Algebra Universalis 48(1): 55-79
11. Cignoli R and Torrens A (2004). Glivenko like theorems in natural expansions of BCK-logics. Math Log Quart 50(2): 111-125
12. 2. Stud Log 83: 157-181
13. Cintula P, Hájek P, Horcik R (2007) Fragments of some prominent fuzzy logics. Manuscript (submitted)
14. Di Nola A, Georgescu G and Leustean L (2000). Boolean products of BL-algebras. J Math Anal Appl 251(1): 106-131
15. Dziobiak W (1989). Finitely generated congruence distributive quasivarieties of algebras. Fundam Math 133: 47-57
16. Font JM, Rodriguez AJ, Torrens A (1984) Wajsberg algebras. Stochastica 8:5-31
17. García FM and Rodriguez AJ (2000). Linearization of BCK-logic. Stud Log 65: 31-51
18. Gispert J and Torrens A (2007). Bounded BCK-algebras and their generated variety. Math Log Q 53: 206-213
19. Grišin VN (1982). Predicate and set-theoretical calculi based on logic without contractions. Math USSR Izv 18: 41-59
20. 0-algebras by means of identities. Math Notes 38: 861-867
21. Iseki K (1966). An algebra related with a propositional calculus. Poc Jpn Acad 42: 26-29
22. Iseki K (1976) On bounded BCK-algebras. Math Sem Notes Kobe Univ 3:23-33 (see also pp 34-36)
23. Iseky K and Tanaka S (1978). An introduction to the theory of BCK-algebras. Math Jpn Acad 23: 1-26
24. Krauss HP, Clark DM (1979) Global subdirect products. Mem Amer Math Soc 210
25. Pałasińska K (1987). Amalgamation property in some classes of BCK-algebras. Rep Math Log 21: 72-84
26. Pałasiński M (1980). Some remarks on BCK-algebras. Math Semmin Notes Kobe Univ 8: 137-144
27. Pałasiński M (1981). On ideal, congruence lattices of BCK-algebras. Math Jpn 26: 543-544
28. Rasiowa H (1974). An algebraic approach to non-classical logics. North Holland, Amsterdam
29. Swamy UM and Suryanarayana G (1981). Murti Boolean centre of universal algebra. Algebra Universalis 13: 202-205
30. Torrens A (1987). W-algebras which are Boolean products of members of SR [1] and CW-algebras. Stud Log 44: 265-274
31. Vaggione D (2000). Characterization of discriminator varieties. Proc Am Math Soc 129: 663-666
32. Wroński A (1983a). BCK algebras do not form a variety. Math Jpn 28: 211-213
33. Wroński A (1983b). Reflections and Distentiones of BCK algebras. Math Jpn 28: 215-225