Optimal query answering in fuzzy knowledge bases

Under a fuzzy knowledge base (f.k.b.) we mean a finite set of formulas of the Zadeh's propositional fuzzy logic (based on a triangular norm min{x, y}). A sentence is a formula with lower and upper bounds - truth values from [0,1]. A state ¿ of f.k.b. S is the sentences set which is obtained by an assignment of lower and upper truth value bounds to each formula of S. A query ¿ to f.k.b state ¿ is a formula with atoms occurring in S. An answer to the query ¿ is a sentence a which logically follows from ¿. The optimal query answer is the answer with the closest bounds. We consider the problem of finding optimal query answers to f.t.b. states. The problem can be by analytical tableaux method. The method results in an algorithm with the exponential worst-case estimate (relatively to the size of ¿
^¿
{¿}). But computation of optimal answers can be sped up considerably when S and ¿ are fixed and ¿ is an arbitrary state of f.k.b. S. Really, consider the general state ¿0 i.e. a state with bounds which are not specific values but parameters (indeterminate values). Then it is possible to find the general optimal answer a to query ¿ to the general state ¿0 This answer has the bounds that are expressions composed from the parameters, and any specific general answer can be obtained by assignments of specific values to the parameters.