Managing uncertainty during the knowledge engineering process from elicitation to validation and verification requires a flexible, intuitive, and semantically sound knowledge representation. This is especially important since this process is typically highly interactive with the human user to add, update, and maintain knowledge. In this paper, we present a model of knowledge representation called Bayesian Knowledge-Bases (BKBs). It unifies a ‘if-then’ style rules with probability theory. We also consider the computational efficiency of reasoning over BKBs. We can show that through careful construction of the knowledge-base, reasoning is computationally tractable and can in fact be polynomial-time. BKBs are currently fielded in the PESKI intelligent system development environment.

In this paper, a systematic theory of the “state-splitting” technique for the decomposition of stochastic machines is presented, which makes use of a stochastic generalization of the conventional concept of covers or set systems.

In this note we show that the family of languages generated by general two-type bracketed grammars coincides with the family of recursively enumerable languages.

In the present paper, an algebraic structure theory of stochastic machines is developed which contains both Bacon's theory [1] and Hartmanis' theory for deterministic machines [5] as special cases. Although the present theory is patterned after both theories, it exhibits many interesting features which are here-to-fore unknown. Among other things, it is shown that the basic concepts involved, e.g., partitions with substitution property, partition pairs, state-behavior realizations, are all equivalent to well-known concepts in linear algebra. Section II introduces the model of stochastic machines to be used in subsequent developments. In Section III, various types of realizations and assignments are introduced. The concepts of partitions with substitution property, partition pairs, etc. are introduced in Section III. The last section gives a formulation of a network of concurrently operating QSMs.