An Axiom Foundation for Uncertain Reasonings in Rule-Based Expert Systems: NT-Algebra

摘要

This paper identifies an axiom foundation for uncertain reasonings in rule-based expert systems: a near topological algebra (NT-algebra for short), which holds some basic notions hidden behind the uncertain reasoning models in rule-based expert systems. According to the basic means of topological connection in an inference network, an NT-algebraic structure has five basic operators, i.e. AND, OR, NOT, Sequential combination and Parallel combination, which obey some axioms. An NT-algebraic structure is defined on a near-degree space introduced by the authors, which is a special topological space. The continuities of real functions, of fuzzy functions and functions in other senses can be uniformly considered in the framework of a near-degree space. This paper also proves that EMYCIN’s and PROSPECTOR’s uncertain reasoning models correspond to good NT-algebras. Moreover, the existence of any finite NT-algebraic structure is constructively proved. Compared to other related research efforts, the NT-algebra as an axiom foundation has the following characteristics: (1) various cases of assessments for uncertainties of evidence and rules are put into a unified algebraic structure; and (2) major emphasis has been placed on the basic laws of the propagation for them in an inference network, especially the continuity of propagation operations and the relationships between propagation operations.