Axiomatizations of Fuzzy Attribute Logic
نویسندگان
چکیده
We study fuzzy attribute logic, i.e. a logic for reasoning about formulas of the form A ⇒ B where A and B are fuzzy sets (non-sharp collections) of attributes. A formula A ⇒ 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 ⇒ B and prove completeness in Pavelka style (graded completeness) which says that a degree to which A ⇒ B semantically follows from T equals a degree to which A ⇒ B is provable from T .
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