Handling inconsistency in partially preordered ontologies: the Elect method

Abstract

We focus on the problem of handling inconsistency in lightweight ontologies. We assume that the terminological knowledge base (TBox) is specified in DL-Lite and that the set of assertional facts (ABox) is partially preordered and may be inconsistent with respect to the TBox. One of the main contributions of this paper is the provision of an efficient and safe method, called Elect, to restore the consistency of the ABox with respect to the TBox. In the case where the assertional base is flat (i.e. no priorities are associated with the ABox) or totally preordered, we show that our method collapses with the well-known intersection ABox repair semantics and the non-defeated semantics, respectively. The semantic justification of the Elect method is obtained by first viewing a partially preordered ABox as a family of totally preordered ABoxes and then applying non-defeated inference to each of the totally preordered ABoxes. We introduce the notion of elected assertions which allows us to provide an equivalent characterization of the Elect method without explicitly generating all the totally preordered ABoxes. We show that computing the set of elected assertions is done in polynomial time with respect to the size of the ABox. The second part of the paper discusses how to go beyond the Elect method. In particular, we discuss to what extent the Elect method can be generalized to description logics that are more expressive than DL-Lite.

Characterizing the Possibilistic Repair for Inconsistent Partially Ordered Assertions

“…Given two assertions (φ i , u i ), (φ j , u j ) ∈ A ▷ , we write φ i ▷ φ j to mean u i ▷ u j (i.e., φ i is strictly preferred to φ j ), and write φ i ▷◁ φ j to mean u i ▷◁ u j (i.e., φ i and φ j are incomparable). Note that the relation ▷ on U is a strict partial order 4 . However, the ABox A ▷ is partially preordered because the same weight can be assigned to more than one assertion.…”

Conflict-Based Inconsistency-Tolerant Query Answering

“…Most of these semantics, inspired by database reparation (Bertossi 2019) or nonmonotonic reasoning in propositional logic, consist in getting rid of inconsistency by first computing a set of (maximally) consistent subsets of the assertional base, called repairs, and then using them to perform query answering. For example, the AR semantics (Lembo et al 2010;Belabbes, Benferhat, and Chomicki 2021) consists in computing all the inclusionmaximal subsets of data that are consistent with the ontology and considering an answer as valid if it holds all the repairs. In (Baget et al 2016), a general framework that unifies inconsistency-tolerant semantics is defined.…”