Parametrization of knowledge structures
type: Item
instance of: scholarly article
title: Parametrization of knowledge structures
zbMATH Open document ID: 0688.68086
DOI: 10.1016/0166-218X(88)90046-7
author: Jean-Paul Doignon
author: Jean-Claude Falmagne
published in: Discrete Applied Mathematics
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 68T99
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 4128432
zbMATH Keywords: quasi-order
zbMATH Keywords: intricacy of a knowledge structure
zbMATH Keywords: surmise system
zbMATH Keywords: weak orders
reviewed by: Wiktor Bartol
MaRDI profile type: Publication
cites work: Rings of sets
cites work: Q5331549
cites work: Q5581652
cites work: Languages for the assessment of knowledge
cites work: A decomposition theorem for partially ordered sets
cites work: Spaces for the assessment of knowledge
cites work: On realizable biorders and the biorder dimension of a relation
cites work: Composite measurement
cites work: A class of stochastic procedures for the assessment of knowledge
cites work: A Markovian procedure for assessing the state of a system
cites work: Axiomatic convexity theory and relationships between the Carathéodory, Helly, and Radon numbers
cites work: On the Dimension of Partially Ordered Sets
cites work: Q4116480
cites work: Q5606610
cites work: Measurement Theory
cites work: Q3948238
cites work: Minimal scrambling sets of simple orders
description: scientific article; zbMATH DE number 4128432