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Notes on Complexity of Monoidal T-norm Based Logic and its Extensions
by
Rostislav Horcik
Institute of Computer Science, Academy of Sciences of the Czech Republic
Coauthors: Marta Bilkova
In this talk we will discuss complexity of many-valued logics which are based on left-continuous t-norms; so-called Monoidal t-norm Logic (MTL) and its axiomatic extensions. There are relatively many complexity results for t-norm based many-valued logics but all these results concern only logics with continuous t-norms (i.e., logics like Lukasiewicz, Gödel, or Hájek’s Basic Fuzzy Logic). The complexity questions for the logics with left-continuous t-norms (i.e., logics between MTL and BL) remain still open. So far there are only decidability results on these logics.
It seems that the complete solution of complexity issues for these logics is a quite difficult task. Thus we are going to present in this talk several possible ways how to attack these problems. We will consider several axiomatic extensions for which it is easier to develop decision procedures. In particular, we will discuss the extensions of MTL by a class of axioms expressing restricted divisibility and the axiom of cancellativity.
Date received: May 11, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caug-40.