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A logical approach for direct-optimal basis of implications. (English) Zbl 1409.68285

Summary: In formal concept analysis, knowledge extracted from a data set is represented in two alternative ways: concept lattices and sets of implications. The sets of implications are optimized under different criteria linked to several properties. In this paper, the optimization task is strongly based on the simplification logic. Specifically, we present a review of how minimal sets of implications (basis) with different properties can be calculated with a logical style. Therefore, different techniques to manipulate them are out-lined. Our logic-based approach property fits with the logic programming paradigm and, thus, a prolog implementation to calculate direct basis from a set of implications is also sketched.

MSC:

68T30 Knowledge representation
68T27 Logic in artificial intelligence
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