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Spaces for the assessment of knowledge. (English) Zbl 0581.68066

The information regarding a particular field of knowledge is conceptualized as a large, specified set of questions (or problems). The knowledge state of an individual with respect to that domain is formalized as the subset of all the questions that this individual is capable of solving. A particularly appealing postulate on the family of all possible knowledge states is that it is closed under arbitrary unions. A family of sets satisfying this condition is called a knowledge space. Generalizing a theorem of Birkhoff on partial orders, we show that knowledge spaces are in a one-to-one correspondence with AND/OR graphs of a particular kind. Two types of economical representations of knowledge spaces are analysed: bases, and Hasse systems, a concept generalizing that of a Hasse diagram of a partial order. The structures analysed here provide the foundation for later work on algorithmic procedures for the assessment of knowledge.

MSC:

68T99 Artificial intelligence
06A06 Partial orders, general
68R10 Graph theory (including graph drawing) in computer science
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