About: Axiomatizations of fuzzy attribute logic

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Description	We study fuzzy attribute logic, i.e. a logic for reasoning about formulas of the form $A\Rightarrow B$ where $A$ and $B$ are fuzzy sets (non-sharp collections) of attributes. A formula $A\Rightarrow B$ is true in a data table with fuzzy attributes iff each object having all attributes from $A$ has also all attributes from $B$, membership degrees of $A$ and $B$ playing a role of thresholds. We present a set of axioms and prove syntactico-semantical completeness with respect to the data table semantics. We also prove some derived rules in our axiomatic system. Furthermore, we introduce a notion of a degree to which a fuzzy set $T$ of formulas entails a formula $A\Rightarrow B$ and prove completeness in Pavelka style (graded completeness) which says that a degree to which $A\Rightarrow B$ semantically follows from $T$ equals a degree to which $A\Rightarrow B$ is provable from $T$. We study fuzzy attribute logic, i.e. a logic for reasoning about formulas of the form $A\Rightarrow B$ where $A$ and $B$ are fuzzy sets (non-sharp collections) of attributes. A formula $A\Rightarrow B$ is true in a data table with fuzzy attributes iff each object having all attributes from $A$ has also all attributes from $B$, membership degrees of $A$ and $B$ playing a role of thresholds. We present a set of axioms and prove syntactico-semantical completeness with respect to the data table semantics. We also prove some derived rules in our axiomatic system. Furthermore, we introduce a notion of a degree to which a fuzzy set $T$ of formulas entails a formula $A\Rightarrow B$ and prove completeness in Pavelka style (graded completeness) which says that a degree to which $A\Rightarrow B$ semantically follows from $T$ equals a degree to which $A\Rightarrow B$ is provable from $T$. (en)
Title	Axiomatizations of fuzzy attribute logic Axiomatizations of fuzzy attribute logic (en)
skos:prefLabel	Axiomatizations of fuzzy attribute logic Axiomatizations of fuzzy attribute logic (en)
skos:notation	RIV/61989592:15310/05:00002093!RIV10-MSM-15310___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM6198959214)
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Vychodil, Vilém Bělohlávek, Radim
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Palackého v Olomouci / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	513451
http://linked.open...ai/riv/idVysledku	RIV/61989592:15310/05:00002093
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Axiomatizations; fuzzy attribute logic (en)
http://linked.open.../riv/klicoveSlovo	Axiomatizations fuzzy attribute logic
http://linked.open...ontrolniKodProRIV	[6FD87D59445D]
http://linked.open...i/riv/mistoVydani	Pune, India
http://linked.open...i/riv/nazevZdroje	Proceedings of 2nd Indian International Conference on Artificial Intelligence
http://linked.open...in/vavai/riv/obor	BD
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2005
http://linked.open...iv/tvurceVysledku	Bělohlávek, Radim Vychodil, Vilém
http://linked.open...n/vavai/riv/zamer	Matematické modely a struktury
number of pages	2280 (xsd:int)
http://purl.org/ne...btex#hasPublisher	Indian International Conference on Artificial Intelligence
https://schema.org/isbn	0-9727412-1-6
http://localhost/t...ganizacniJednotka	15310

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