Open theories, consistency and related results in fuzzy logic

The paper deals with fuzzy logic in the narrow sense of Lukasiewicz style, i.e. a special kind of many-valued logic which is aimed at modeling of vagueness phenomenon. This logic is a generalization of Lukasiewicz logic with many interesting properties (for example, generalization of the deduction and completeness theorems hold in it). Our aim is to prepare the background for the resolution in fuzzy logic. We prove an analogue of the classical Herbrand theorem as well as some other related theorems which are interesting also for the theory of approximate reasoning. The possible applications and consequences for the latter are also discussed.