How Much Knowledge is in a Knowledge Base? Introducing Knowledge Measures (Preliminary Report)

In this work we address the following question: can we measure how much knowledge a knowledge base represents? We answer to this question (i) by describing properties (axioms) that a knowledge measure we believe should have in measuring the amount of knowledge of a knowledge base (kb); and (ii) provide a concrete example of such a measure, based on the notion of entropy. We also introduce related kb notions such as (i) accuracy; (ii) conciseness; and (iii) Pareto optimality. Informally, they address the following questions: (i) how precise is a kb in describing the actual world? (ii) how succinct is a kb w.r.t. the knowledge it represents? and (iii) can we increase accuracy without decreasing conciseness, or vice-versa?