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...

• Type: Conference
• Year: 2007
• Where: ICCS
• Authors: José L. Balcázar, Gemma C. Garriga
• Keywords: Conceptual Structures, Deterministic Association Rules, ICCS 2007, Partial Orders