From information to probability: An axiomatic approach - Inference isinformation processing

We define the very rich language of composed conditionals on a three-valued logic and use this language as the communication tool between man and machine. Communication takes place for three reasons: Knowledge acquisition, query and response. Learning, thinking and answering questions are of pure information theoretical nature. The pivot of this knowledge processing concept is the amount of information in [bit] which we receive, if we learn a conditional to become true. We follow an axiomatic approach to information theory rather than the classical probabilistic approach of Shannon; information comes first, then comes probability. In the light of this philosophy query and response experience new interpretations. Both, acquisition and response are realized by maximizing entropy and minimizing relative entropy, respectively. The iterative solution of these mathematical optimization problems gives new insights into the adaptation of prior knowledge to new information. The expert system shell SPIRIT supports this kind of knowledge processing which will be demonstrated by suitable examples.