Representation of algebraic convex geometries
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Date
2014
Authors
Adaricheva, K.
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University
Abstract
Convex geometry is a set system generated by the closure operator with the antiexchange
axiom. These systems model the concept of convexity in various settings. They are also closely
connected to anti-matroids, which are set systems with the property of accessibility. In particular, the
latter were used in modelling the states of human learners and found practical applications in designing
the automatic tutoring systems. In current work we develop the theoretical foundations of infinite convex
geometries in case their closure operator satisfies the finitary property: closure of any subset is a union of
closures of its finite subsets. In such case, the convex geometry is called algebraic.
Description
Keywords
convex geometries, system, modelling, automatic, algebraic