Incomplete Information and Bayesian Knowledge-Bases

Knowledge acquisition is an essential process in improving the problem-solving capabilities of existing knowledge-based systems through the absorption of new information and facilitating change in current knowledge. However, without a verification mechanism, these changes could result in violations of semantic soundness of the knowledge causing inconsistencies and ultimately, contradictions. Therefore, maintaining semantic consistency is of primary concern, especially when dealing with incompleteness and uncertainty. In this paper, we consider the semantic completability of a knowledge system as a means of ensuring long-term semantic soundness. In particular, we focus on how to preserve semantic completability as the knowledge evolves over time. Among numerous methods of knowledge representation under uncertainty, we examine Bayesian Knowledge-Bases, which are a rule-based probabilistic model that allows for incompleteness and cycles between variables. A formal definition of full/partial completability of BKB is first introduced. A principle to check the overall completability of a BKB is then formulated with a formal proof of correctness. Furthermore, we show how to use this principle as a guide for maintaining semantic soundness and completability during incremental knowledge acquisition. In particular, we consider two primary modifications to the knowledge base: 1) adding/fusing knowledge, and 2) changing/tuning conditional probabilities.