Semantic Filtering with Relational Sample Clauses

Semantic Filtering with Relational. Expressions Now let us assume that the user interests as well as the eMFA contain relational expressions as outlined above. Denoting ai as LUMO-rel con- cepts/topics or LUMO-Pedia named entities, and reli as LUMO-rel relations, the eMFA then has the shape: } eMFA = a1, rel j(a1, a j), relk(a1, ak), . . . , an, rell(ak, al), relm(ak, am), c1, . . . , x x, t1, . . . , tx , (6) i.e., a set of (named) entities with relations to other entities, as well as a set of concepts and topics. Accordingly, we restrict user interests to the same representational means (where all concrete entities are named ones from LUMO-Pedia): ui = ai XXxxx x.x j H... HEreln.an . (7) E The relational filtering further includes Eqns. 2–5, and further a relational expression ai. rel x.x j in the UI, which is entailed by the eMFA if the eMFA contains an expression rel j (X,Y ) and X entails the anchor term ai and Y the a j: eMFA |=LUMO-rel Xxxx x.x j iff rel(X,Y ) ∈ eMFA ΛX |=LUMO-rel ai ΛYej |=LUMO-rel a j (8) This reasoning can straightforwardly be extended towards more complex user interests (with con- junctions and disjunctions, relational concatenations, data properties and constraints on data in user interests, etc.). The current version is mainly determined by the restrictions we have on the user interest and the MF annotation side, and by efficiency considerations. The more complex the expressions are the more complex is the reasoning.‌
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