Query answering over fact bases in fuzzy propositional logic

摘要

Let L be a fuzzy propositional logic based on triangular norm min(x,y) (Zadeh's logic). A fact in L is an expression of the form r ≤ ϕ; ≤ s where ϕ; ∈ L and 0 ≤ r ≤ s ≤ 1. In fuzzy interpretation I of L every fact is true or false, and I(r ≤ ϕ; ≤ s) = 1 if and only if the two-side inequality r ≤ I(ϕ;) ≤ s is satisfied. Thus, the set FL of all facts defines a crisp logic with fuzzy interpretations. Logical consequence “|=” in the logic FL is defined as usual: for any set E of facts and any fact a, E |= α if there are no an interpretation I and a fact β ∈ E such that I(α) = 1 and I(β) = 0‥ But in the logic FL there is also strong logical consequence |=*: E |=* r ≤ ϕ; ≤ s if E |= r ≤ ϕ; ≤ s and it is not true that E |= r′ ≤ ϕ; ≤ s with r′> r and not true E |= r ≤ ϕ; ≤ s′ with s′