On Strong Standard Completeness in Some MTL-Delta Expansions

0466763 - ÚI 2017 RIV DE eng J - Journal Article
Vidal, Amanda - Bou, F. - Esteva, F. - Godo, L.
On Strong Standard Completeness in Some MTL-Delta Expansions.
Soft Computing. Roč. 21, č. 1 (2017), s. 125-147. ISSN 1432-7643. E-ISSN 1433-7479
R&D Projects: GA ČR(CZ) GF15-34650L
Grant - others:Austrian Science Fund(AT) I1897-N25
Institutional support: RVO:67985807
Keywords : mathematical fuzzy logic * left-continuous t-norms * monoidal t-norm logic * infinitary rules * standard completeness
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impact factor: 2.367, year: 2017

In this paper, inspired by the previous work of Franco Montagna on infinitary axiomatizations for standard BL-algebras, we focus on a uniform approach to the following problem: given a left-continuous t-norm *, find an axiomatic system (possibly with infinitary rules) which is strongly complete with respect to the standard algebra [0,1]*. This system will be an expansion of Monoidal t-norm-based logic. First, we introduce an infinitary axiomatic system L, expanding the language with Delta and countably many truth constants, and with only one infinitary inference rule, that is inspired in Takeuti–Titani density rule. Then we show that L is indeed strongly complete with respect to the standard algebra [0,1]*. Moreover, the approach is generalized to axiomatize expansions of these logics with additional operators whose intended semantics over [0,1] satisfy some regularity conditions.
Permanent Link: http://hdl.handle.net/11104/0264998