Knowledge Predicate Logic

Knowledge logic is an important branch of cognitive logic. As far as Plato studied knowledge in ancient Greece, philosophers have studied it. The study on formal system of knowledge logic began with G-Hvon-wright's An Essay in Modal Logic in 1951. While the book--Knowledge and Belief wrote by J·Hintikka first studied knowledge logic in the means of modern logic. Since 1990s', knowledge logic has been studied from different directions: cognitive reasoning about certain cognitive agent, cognitive reasoning about many cognitive agents , cognitive logic paradox and cognitive logic and artificial intelligence……This paper discusses the structure of formal systems of knowledge predicate logic and the consistence and completeness of these systems. Four parts compose the paper, as follows:The first part analyzes knowledge proposition. It chiefly discussed the logical meaning and property of "knowledge". At the same time, it explains some situations of "knowledge" and "agent".The second part analyzes the formal language of knowledge predicate logic. It introduces the initial symbol, formational rule and semantic explain of this language,especially "K_a".The third part is the main body of this paper. In this part, author deeply studies three systems of knowledge predicate logic on the basis of former parts, which are as follows: the system of K_m+K_BF, the system of K_s4+K_BF, the system of K_s5+K_BF, and proves some theorems, consistence and completeness of these systems.The last part discusses some difficulties in the course of building knowledge predicate logic systems: recognizing agents across the worlds; logic almightiness; knowability paradox……...