A computationally grounded logic of knowledge, belief and certainty

This paper presents a logic of knowledge, belief and certainty, which allows us to explicitly express the knowledge, belief and certainty of an agent. A computationally grounded model, called interpreted KBC systems, is given for interpreting this logic. The relationships between knowledge, belief and certainty are explored. In particular, certainty entails belief; and to the agent what it is certain of appears to be the knowledge. To formalize those agents that are able to introspect their own belief and certainty, we identify a subclass of interpreted KBC systems, called introspective KBC systems. We provide sound and complete axiomatizations for the logics. We show that the validity problem for the interpreted KBC systems is PSPACE-complete, and the same problem for introspective KBC systems is co-NP complete, thus no harder than that of the propositional logic. Categories and Subject Descriptors F.3.1 [Logics and Meanings of Programs]: Specifying and Verifying and Reasoning about ...

• Type: Conference
• Year: 2005
• Where: ATAL
• Authors: Kaile Su, Abdul Sattar, Guido Governatori, Qingliang Chen
• Keywords: ATAL 2005, Interpreted Kbc Systems, Introspective Kbc Systems, KBC Systems