On Proofs and Rule of Multiplication in Fuzzy Attribute Logic

Abstract. The paper develops fuzzy attribute logic, i.e. a logic for reasoning about formulas of the form A ⇒ B where A and B are fuzzy sets of attributes. A formula A ⇒ B represents a dependency which 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 in A and B playing a role of thresholds. We study axiomatic systems of fuzzy attribute logic which result by adding a single deduction rule, called a rule of multiplication, to an ordinary system of deduction rules complete w.r.t. bivalent semantics, i.e. to well-known Armstrong axioms. In this paper, we concentrate on the rule of multiplication and its role in fuzzy attribute logic. We show some advantageous properties of the rule of multiplication. In addition, we show that these properties enable us to reduce selected problems concerning proofs in fuzzy attribute logic to the corresponding problems in the ordinary case. As an example, we dis...

• Type: Conference
• Year: 2007
• Where: IFSA
• Authors: Radim Belohlávek, Vilém Vychodil
• Keywords: Artificial Intelligence, Deduction Rules, Fuzzy Attribute Logic, Fuzzy Sets, IFSA 2007