Chinese Journal of Computers   Full Text
Title	Logic for Knowledgebase Systems
Authors	XU Wen-Yan LIU San-Yang
Address	(Department of Mathematic, Institute of Sciences, Xidian University, Xi’an 710071)
Year	2009
Issue	No.11(2123—2129)
Abstract &   Background	Abstract According to the features and requirements of knowledgebase systems, the authors discuss the insufficiency of basing knowledgebase systems on classical first-order logic, and analyze the rationality and sufficiency of basing them on computability logic. The authors apply the method of proof theory and construct an axioms system of knowledgebase system, which is based on a complete subset CL4 of computability logic and shows the simplicity of knowledge representations and convenience of operating.. Keywords computability logic; knowledgebase system; game; interactive; resources Background As the result of combining artificial intelligence and data-base, knowledgebase systems have been one of the topics of most concern. When studying knowledgebase systems, one of considerably important problems is the logic on which the system is based. This paper focuses on this topic. Traditional knowledgebase systems are based on classical first-order logic. But the language of first-order logic only expresses the static and shallow knowledge, not expressing interactive processes and constructive knowledge. So it is not sufficient to base knowledgebase systems on first-order logic. The traditional approaches to knowledgebase systems try to mend this insufficiency by arguing the language of classical logic with special epistemic constructs, such as the modal “know that” operator □. But these epistemic constructs often yield unnecessary and very unpleasant complications such as messiness and non-semidecidability of the resulting logics. Computability logic (CL), introduced recently, is a formal theory of computability. Computation and computational problems in CL are understood in their most general, interactive sense, and are seen as games played by a machine (computer) against its environment (user). Classical logic turns out to be a special fragment of CL. The classical concept of truth is nothing but a special case of computability—computability restricted to problems of zero interactivity degree. This paper analyses the features of knowledgebase systems and the requirements of its logic, discusses the limitations of classical first-order logic and the superiorities of computability logic. Based on a system of computability logic, an axioms system of a knowledgebase system is constructed, which shows the simplicity and preciseness of knowledge representations, efficiency of queries to the system, and convenience of operating. The conclusion is that CL is an appealing alternative to traditional knowledge base. This paper apperceives it and makes an attempt on it. This research is supported by the National Natural Science Foundation of China (grant Nos.60574075, 60674108).