Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A representation of antimatroids by Horn rules and its application to
  educational systems   We study a representation of an antimatroid by Horn rules, motivated by its
recent application to computer-aided educational systems. We associate any set
$\mathcal{R}$ of Horn rules with the unique maximal antimatroid
$\mathcal{A}(\mathcal{R})$ that is contained in the union-closed family
$\mathcal{K}(\mathcal{R})$ naturally determined by ${\cal R}$. We address
algorithmic and Boolean function theoretic aspects on the association ${\cal R}
\mapsto \mathcal{A}(\mathcal{R})$, where ${\cal R}$ is viewed as the input. We
present linear time algorithms to solve the membership problem and the
inference problem for ${\cal A}({\cal R})$. We also provide efficient
algorithms for generating all members and all implicates of ${\cal A}({\cal
R})$. We show that this representation is essentially equivalent to the
Korte-Lov\'{a}sz representation of antimatroids by rooted sets. Based on the
equivalence, we provide a quadratic time algorithm to construct the
uniquely-determined minimal representation. % These results have potential
applications to computer-aided educational systems, where an antimatroid is
used as a model of the space of possible knowledge states of learners, and is
constructed by giving Horn queries to a human expert.

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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: econ