Unranked Fuzzy Logic and Reasoning

One of the main tools in knowledge representation is ontology, which is a collection of logic-based formal language sentences. These sentences are used by automated reasoning programs to extract new knowledge and answer to the given questions. Although ontology languages are standardized by W3C, there are still many problems remaining. One of the most important problems is related to ontologies, where information is vague and incomplete. Such kind of ontologies have applications in many different fields, such as medicine, biology, e-commerce and the like. They require concepts from both, fuzzy and unranked theories. This is a follow-up paper of a one by the authors, where an unranked fuzzy logic was introduced. Here we develop a tableau method for reasoning over such logic. The unranked fuzzy logic is an extension of many-valued logics with sequence variables and flexible-arity function and predicate symbols. The unranked fuzzy tableau calculus corresponds to Hájek’s witnessed fuzzy logics and is therefore complete.