Open theories, consistency and related results in fuzzy logic (Q1818104)

In order to set the background for the resolution method development and application in fuzzy logic, the author considers a generalization of Łukasiewicz first-order logic having many important properties. Namely, it is shown that for this logic the corresponding generalizations of the deduction and completeness theorem hold. In this way a syntactical reasoning on truth values is provided, establishing a formal tool for the modeling of the vagueness phenomenon. As the crucial step approaching resolution, an analogue to the Herbrand theorem is proved as well, providing a good formal basis for resolution in the context of fuzzy logic.