  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.
