In some applications it is necessary to sort a set of elements according to an order relationship which is not known a priori. In these cases, a training set of ordered elements is often available, from which the order relationship can be automatically learned. In this work, it is assumed that the correct succession of elements in a training sequence (or chain) is given, so that it is possible to induce the definition of two predicates, first/1 and succ/2, which are then used to establish an ordering relationship. A peculiarity of this work is the relational representation of training data which allows various relationships between ordered elements to be expressed in addition to the ordering relationship. Therefore, an ILP learning algorithm is applied to induce the definitions of the two predicates. Two methods are reported for the identification of either single chains or multiple chains on new objects. They have been applied to the problem of learning the reading order of layout components extracted from document images. Experimental results show the effectiveness of the proposed solution.
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