On the independence of axioms in BL and MTL

0370261 - ÚI 2013 RIV NL eng J - Journal Article
Chvalovský, Karel
On the independence of axioms in BL and MTL.
Fuzzy Sets and Systems. Roč. 197, 16 June (2012), s. 123-129. ISSN 0165-0114. E-ISSN 1872-6801
R&D Projects: GA ČR GEICC/08/E018; GA ČR GD401/09/H007
Grant - others:GA UK(CZ) 73109/2009
Institutional research plan: CEZ:AV0Z10300504
Keywords : non-classical logics * basic fuzzy logic (BL) * monoidal t-norm based logic (MTL) * Hilbert-style calculi * independence of axioms
Subject RIV: BA - General Mathematics
Impact factor: 1.749, year: 2012

We prove that the axiom expressing that the multiplicative conjunction of two formulae implies the first one of them is redundant in the standard Hilbert-style calculi of Hájek's basic logic BL and Esteva and Godo's monoidal t-norm based logic MTL. This proof does not use the axiom expressing that multiplicative conjunction is commutative, which is already known to be redundant. Therefore both of these axioms are simultaneously redundant. We also show that all the other axioms are independent of each other.
Permanent Link: http://hdl.handle.net/11104/0204111