TY - GEN

AU - Doignon, Jean-Paul

AU - Falmagne, Jean-Claude

TI - Knowledge Spaces

PB - Springer Berlin Heidelberg

SN - 9783642586255

KW - Computer science

KW - Combinatorics

KW - Artificial intelligence

KW - Discrete mathematics.

PY - 1999

N2 - 0. Overview and Mathematical GlossaryMain Concepts -- Possible Limitations -- A Practical Application: The Aleks System -- Potential Applications to Other Fields -- On the Content and Organization of this Book -- Glossary of Mathematical Concepts -- Original Sources and Related Works -- 1. Knowledge Structures and Spaces -- Fundamental Concepts -- Knowledge Spaces -- Closure Spaces -- Substructures -- Bases and Atoms -- An Algorithm for Constructing the Base -- An Algorithm for Generating a Space from its Base -- Bases and Atoms: the Infinite Case* -- The Surmise Relation -- Quasi Ordinal Spaces -- Original Sources and Related Works -- Problems -- 2. Well-Graded Knowledge Structures -- Essentially Finite Structures -- A Well-Graded Family of Relations: the Biorders* -- The Infinite Case* -- Finite Learnability -- Original Sources and Related Works -- Problems -- 3. Surmise Systems -- Basic Concepts -- Knowledge Spaces and Surmise Systems -- AND/OR Graphs -- Surmise Functions and Wellgradedness -- Hasse Systems -- Resolubility and Acyclicity -- Original Sources and Related Works -- Problems -- 4. Skill Maps, Labels and Filters -- Skills -- Skill Maps: The Disjunctive Model -- Minimal Skill Maps -- Skill Maps: The Conjunctive Model -- Skill Multimaps: The Competency Model -- Labels and Filters -- Original Sources and Related Works -- Problems -- 5. Entailments and the Maximal Mesh -- Entailments -- Entail Relations -- Meshability of Knowledge Structures -- The Maximal Mesh -- Original Sources and Related Works -- Problems -- 6. Galois Connections* -- Three Exemplary Correspondences -- Closure Operators and Galois Connections -- Lattices and Galois Connections -- Knowledge Structures and Binary Relations -- Granular Knowledge Structures and Granular Attributions -- Knowledge Structures and Associations -- Original Sources and Related Works -- Problems -- 7. Probabilistic Knowledge Structures -- Basic Concepts and Examples -- An Empirical Application -- The Likelihood Ratio Procedure -- Learning Models -- A Combinatorial Result -- Markov Chain Models -- Probabilistic Substructures -- Nomenclatures and Classifications -- Independent Substructures -- Original Sources and Related Works -- Problems -- 8. Stochastic Learning Paths -- A Knowledge Structure in Euclidean Geometry -- Basic Concepts -- Basic Results -- Assumptions on Distributions -- The Learning Latencies -- Empirical Predictions -- Limitations of this Theory -- Simplifying Assumptions -- Remarks on Application and Use of the Theory -- An Application of the Theory to the Case n =2 -- Original Sources and Related Works -- Problems -- 9. Descriptive and Assessment Languages -- Languages and Decision Trees -- Terminology -- Recovering Ordinal Knowledge Structures -- Recovering Knowledge Structures -- Original Sources and Related Works -- Problems -- 10. Uncovering the State of an Individual: A Continuous Markov Procedure -- A Deterministic Algorithm -- Outline of a Markovian Stochastic Process -- Notation and Basic Concepts -- Special Cases -- General Results -- Uncovering the Latent State -- Refining the Assessment -- Proofs* -- Original Sources and Related Works -- Problems -- 11. Uncovering the State of an Individual: A Markov Chain Procedure -- Outline of a Markov Chain Procedure -- The Stochastic Assessment Process -- Combinatorial Assumptions on the Structure -- Markov Chains Terminology -- Results for the Fair Case -- Uncovering a Stochastic State: Examples -- Intractable Case -- Original Sources and Related Works -- Problems -- 12. Building the Knowledge Structure in Practice -- Koppen’s Algorithm for Constructing the Knowledge Space -- Kambouri’s Experiment -- Results -- Discussion of Kambouri’s Results -- Cosyn and Thiéry’s Work -- Refining a Knowledge Structure -- Simulation of Various Refinements -- Original Sources and Related Works -- Problems -- References -- Index of Names -- Index of Terms.

CY - Berlin, Heidelberg

UR - http://slubdd.de/katalog?TN_libero_mab2

ER -

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