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KNOWLEDGE SPACES By Jean-paul Doignon & Jean-claude Falmagne
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eBay item number:226095347016
Item specifics
- Condition
- Good
- Seller notes
- ISBN-10
- 3540645012
- Book Title
- Knowledge Spaces
- ISBN
- 9783540645016
- Subject Area
- Computers, Mathematics
- Publication Name
- Knowledge Spaces
- Publisher
- Springer Berlin / Heidelberg
- Item Length
- 9.3 in
- Subject
- Natural Language Processing, Intelligence (Ai) & Semantics, Discrete Mathematics
- Publication Year
- 1998
- Type
- Textbook
- Format
- Trade Paperback
- Language
- English
- Item Height
- 0.3 in
- Item Weight
- 38.8 Oz
- Item Width
- 6.1 in
- Number of Pages
- Xvi, 334 Pages
About this product
Product Information
Knowledge spaces offer a rigorous mathematical foundation for various practical systems of knowledge assessment. An example is offered by the ALEKS system (Assessment and LEarning in Knowledge Spaces), a software for the assessment of mathematical knowledge. From a mathematical standpoint, knowledge spaces generalize partially ordered sets. They are investigated both from a combinatorial and a stochastic viewpoint. The results are applied to real and simulated data. The book gives a systematic presentation of research and extends the results to new situations. It is of interest to mathematically oriented readers in education, computer science and combinatorics at research and graduate levels. The text contains numerous examples and exercises and an extensive bibliography.
Product Identifiers
Publisher
Springer Berlin / Heidelberg
ISBN-10
3540645012
ISBN-13
9783540645016
eBay Product ID (ePID)
230781
Product Key Features
Number of Pages
Xvi, 334 Pages
Language
English
Publication Name
Knowledge Spaces
Publication Year
1998
Subject
Natural Language Processing, Intelligence (Ai) & Semantics, Discrete Mathematics
Type
Textbook
Subject Area
Computers, Mathematics
Format
Trade Paperback
Dimensions
Item Height
0.3 in
Item Weight
38.8 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
98-029442
Number of Volumes
1 Vol.
Illustrated
Yes
Dewey Decimal
006.3/5
Lc Classification Number
Qa297.4
Table of Content
0. Overview and Mathematical Glossary.- Main 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.
Copyright Date
1999
Item description from the seller
Seller assumes all responsibility for this listing.
eBay item number:226095347016
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