Parametrization of knowledge structures (Q1264001)

Several numerical parameters are introduced (or generalized) in order to measure the intricacy of a knowledge structure. This last notion is also generalized in the paper in the sense that it is induced by a surmise system instead of a quasiordering of knowledge, where a surmise system is a mapping s which to every elementary question x in a body of knowledge X associates a nonempty family s(x) of subsets of X called clauses for x. A typical example of a characterization of a parameter considered in the paper can be (for finite X) Proposition 3.10: The separating number of a space-like surmise system (X,s) is the least number of weak orders \((X,W_ i)\) satisfying, for every x in X, (i) for all indices i, there is a clause \(C\in s(x)\) such that \(C\subseteq W_ i(x)\), (ii) \(\cap s(x)=\cap_{i}W_ i(x).\) The last section of the paper contains results comparing different parameters.