Pavelka-style fuzzy logic for attribute implications

Authors

Radim Belohlavek ⁰, Vilem Vychodil

Corresponding Author

Radim Belohlavek

DOI

https://doi.org/10.2991/jcis.2006.282How to use a DOI?

Keywords

attribute dependency, fuzzy logic, attribute implication, Armstrong axioms, graded completeness

Abstract

We present Pavelka-style fuzzy logic for reasoning about attribute implications, i.e. formulas $A\Rightarrow B$. Fuzzy attribute implications allow for two different interpretations, namely, in data tables with graded (fuzzy) attributes and in data tables over domains with similarity relations. The axioms of our logic are inspired by well-known Armstrong axioms but the logic allows us to infer partially true formulas from partially true formulas. We prove soundness and completeness of our logic in graded style, i.e. we prove that a degree to which an attribute implication $A\Rightarrow B$ semantically follows from a collection $T$ of partially true attribute implications equals a degree to which $A\Rightarrow B$ is provable from $T$.

Open Access

This is an open access article distributed under the CC BY-NC license.