2020-05-29T23:34:39Z
http://digital.csic.es/dspace-oai/request
oai:digital.csic.es:10261/160601
2018-08-09T10:11:13Z
com_10261_60
com_10261_4
col_10261_313
Esteva, Francesc
Godo, Lluis
Hajek, Petr
Montagna, Franco
2018-02-13T14:25:50Z
2018-02-13T14:25:50Z
2003
Journal of Logic and Computation 13: 531- 555 (2003)
http://hdl.handle.net/10261/160601
http://dx.doi.org/10.13039/501100007273
In this paper we investigate the falsehood-free fragments of main residuated fuzzy logics related to continuous t-norms (HaÌ?jek's Basic fuzzy logic BL and some well-known axiomatic extensions), and we relate them to the varieties of 0-free subreducts of the corresponding algebras. These turn out to be classes of algebraic structures known as hoops. We provide axiomatizations of all these fragments and we call them hoop logics; we prove they are strongly complete with respect to their corresponding classes of hoops, and that each fuzzy logic is a conservative extension of the corresponding hoop logic. Analogously, we also study the falsehood-free fragment of a weaker logic than BL, called MTL, which is the logic of left-continuous t-norms and their residua, and we introduce the related algebraic structures which are called semihoops. Moreover, we also consider the falsehood-free fragments of the fuzzy predicate calculi of the above logics and show completeness and conservativeness results. The role of axiom (âˆ€3) in these predicate logics is studied. Finally, computational complexity issues of the prepositional logics are also addressed.
eng
closedAccess
Mathematical fuzzy logics
Hoops
Falsehood-free fragments
Conservativeness
BL-algebras
Hoops and fuzzy logic
artículo