On the independence of axioms in BL and MTL

  • Authors:

  • Karel Chvalovský

  • Affiliations:

  • Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07 Prague 8, Czech Republic and Department of Logic, Charles University, C ...

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2012

Quantified Score

Hi-index 0.20

Visualization

Abstract

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 Hajek'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.