Characterizing Implications of Injective Partial Orders

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Characterizing Implications of Injective Partial Orders
Abstract. Previous work of the authors has studied a notion of implication between sets of sequences based on the conceptual structure of a Galois lattice, and also a way of representing sets of sequences as partial orders. However, a characterization of implications between partial orders has remained elusive. Here we focus on the somewhat simplified problem of implications between rankings, that is, injective partial orders, where a complete, mathematically verified theory exists. We propose a quite standard Galois connection and a quite standard form of constructed implications (namely, deterministic association rules) as a form of data-mining-like process on partially ordered data, modeled as transitive-closed labeled graphs with injective labelings. We prove that our proposed rules can be formally justified by a purely logical characterization, namely, a natural notion of empirical Horn approximation for partially ordered data, which involves background Horn conditions quite di...
José L. Balcázar, Gemma C. Garriga
Added 08 Jun 2010
Updated 08 Jun 2010
Type Conference
Year 2007
Where ICCS
Authors José L. Balcázar, Gemma C. Garriga
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