9th Joint International Conference on Information Sciences (JCIS-06)

Pavelka-style fuzzy logic for attribute implications

Authors
Radim Belohlavek 0, Vilem Vychodil
Corresponding Author
Radim Belohlavek
0Palacky University
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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 $T$.
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Proceedings
9th Joint International Conference on Information Sciences (JCIS-06)
Publication Date
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ISBN
978-90-78677-01-7
DOI
https://doi.org/10.2991/jcis.2006.282How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - CONF
AU  - Radim Belohlavek
AU  - Vilem Vychodil
PY  - NaN/NaN
DA  - NaN/NaN
TI  - Pavelka-style fuzzy logic for attribute implications
BT  - 9th Joint International Conference on Information Sciences (JCIS-06)
PB  - Atlantis Press
UR  - https://doi.org/10.2991/jcis.2006.282
DO  - https://doi.org/10.2991/jcis.2006.282
ID  - BelohlavekNaN/NaN
ER  -