Abstract:

Based on the basis system L*, a schematic extension BL_Δ* is introduced by adding the unary connective　Δ to BL* with the idea of Petr Hájek.The concept of Δ-root of theory in BL_Δ*is proposed and basic properties of Δ-roots are investigated. Particularly, the problems of generalized Δ-modus ponens and collectively generalized Δ-modus ponens are proposed, and the syntactic solutions of them are defined and the existence of solutions is discussed.

Key words:  fuzzy logic; basis system L*; unary connective Δ;Δ-root; generalized modus ponens problem