Provenance for the Description Logic ELHr

Abstract

<jats:p>We address the problem of handling provenance information in ELHr ontologies. We consider a setting recently introduced for ontology-based data access, based on semirings and extending classical data provenance, in which ontology axioms are annotated with provenance tokens. A consequence inherits the provenance of the axioms involved in deriving it, yielding a provenance polynomial as an annotation. We analyse the semantics for the ELHr case and show that the presence of conjunctions poses various difficulties for handling provenance, some of which are mitigated by assuming multiplicative idempotency of the semiring. Under this assumption, we study three problems: ontology completion with provenance, computing the set of relevant axioms for a consequence, and query answering.</jats:p>

An Upper Bound for Provenance in ELHr

“…An ELH r TBox is a finite set of ELH r axioms. The reason for syntactically restricting ELH r is that conjunctions or qualified restrictions of a role on the right-hand side of GCIs lead to counter-intuitive behavior when adding provenance annotations; see [5] for a detailed discussion on this issue.…”

“…Very recently, the problem of answering provenance queries in the description logic ELH r was studied [5]. That work focused on a semiring where the product operation is commutative and idempotent, and expressed the provenance information through an expanded polynomial; that is, a sum of monomials.…”

“…In this paper we improve that upper bound by showing that the monomial for a subsumption problem is in NP. To achieve this goal, we view the completion algorithm from [5] as a weighted tree automaton, which accepts all the completion-like proofs of a derivation. Through the behaviour of this automaton, the monomial problem is reduced to a membership problem in regular languages.…”

Generalized Completeness for SOS Resolution and its Application to a New Notion of Relevance

“…The notion of a minimal unsatisfiable core does not provide a test for semi-relevance of a specific clause. There are various notions from the description logic community related to unsatisfiable cores of a translation to first-order and/or to our notion of relevance [1,4,8,16]. An in-depth discussion of these relationships can be found in our description logic workshop paper [7].…”

Semiring Provenance for Büchi Games: Strategy Analysis with Absorptive Polynomials

“…The overall value of the formula is then a polynomial that describes precisely what combinations of literals prove the truth of the formula. Semiring semantics has been studied for various logics [1,7,8,9,15], following the successful development of semiring provenance in database theory and related fields (see e.g. [10,12,18,19,23,24,25]).…”