Fuzzy four-valued logic for inconsistency and uncertainty

A logic with truth values represented by points in the unit square is developed. The logic is simultaneously a strict generalization of Belnap's four-valued logic for handling inconsistency and of Zadeh's fuzzy logic for handling uncertainty. The logic can be used for a question answering system or data base of fuzzy information in which inconsistent data may appear but should not result in everything being reported as true.