Computational complexity of t-norm based propositional fuzzy logics with rational truth constants

Authors:
Petr Hájek
Affiliations:
Institute of Computer Science, Academy of Sciences of the Czech Republic, 182 07 Prague, Czech Republic
Venue:
Fuzzy Sets and Systems
Year:
2006

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Abstract

If a continuous t-norm on [0,1] maps pairs of rationals into rationals then the corresponding fuzzy propositional calculus can be extended by rational truth constants and ''bookkeeping'' axioms for them. (Lukasiewicz t-norm is the classical example.) Computational complexity of such logics is studied. Consequences for fuzzy description logic are formulated.