Reasoning complexity for extended fuzzy description logic with qualifying number restriction

To solve the extended fuzzy description logic with qualifying number restriction （EFALCQ） reasoning problems, EFALCQ is discretely simulated by description logic with qualifying number restriction （ALCQ）, and ALCQ reasoning results are reused to prove the complexity of EFALCQ reasoning problems. The ALCQ simulation method for the consistency of EFALCQ is proposed. This method reduces EFALCQ satisfiability into EFALCQ consistency, and uses EFALCQ satisfiability to discretely simulate EFALCQ satdomain. It is proved that the reasoning complexity for EFALCQ satisfiability, consistency and sat-domain is PSPACE-complete.

A Dynamic Fuzzy Description Logic

Fuzzy description logics are considered as the logical infrastructure of fuzzy knowledge representation on the semantic Web. To deal with fuzzy and dynamic knowledge on the semantic Web and its applications, a new fuzzy extension of Attribute Language with Complement based on dynamic fuzzy logic called the dynamic fuzzy description logic （DFALC） is presented. The syntax and semantics of DFALC are formally defined, and the forms of axioms and assertions are specified. The DFALC provides more reasonable logic foundation for the semantic Web, and overcomes the insufficiency of using fuzzy description logic FALC to act as logical foundation for the semantic Web. The extended DFALC is more expressive than the existing fuzzy description logics and present more fuzzy information on the semantic Web.

Capability requirements modeling and verification based on fuzzy ontology

The capability requirements of the command, control, communication, computing, intelligence, surveillance, reconnaissance （C41SR） systems are full of uncertain and vague information, which makes it difficult to model the C41SR architecture. The paper presents an approach to modeling the capability requirements with the fuzzy unified modeling language （UML） and building domain ontologies with fuzzy description logic （DL）. The UML modeling constructs are extended according to the meta model of Depart- ment of Defense Architecture Framework to improve their domain applicability, the fuzzy modeling mechanism is introduced to model the fuzzy efficiency features of capabilities, and the capability requirement models are converted into ontologies formalized in fuzzy DL so that the model consistency and reasonability can be checked with a DL reasoning system. Finally, a case study of C41SR capability requirements model checking is provided to demonstrate the availability and applicability of the method.

New reasoning algorithm based on EFALC

The current extended fuzzy description logics lack reasoning algorithms with TBoxes. The problem of the satisfiability of the extended fuzzy description logic EFALC cut concepts w. r. t. TBoxes is proposed, and a reasoning algorithm is given. This algorithm is designed in the style of tableau algorithms, which is usually used in classical description logics. The transformation rules and the process of this algorithm is described and optimized with three main techniques： recursive procedure call, branch cutting and introducing sets of mesne results. The optimized algorithm is proved sound, complete and with an EXPTime complexity, and the satisfiability problem is EXPTime-complete.