Signature-Based Abduction for Expressive Description Logics

Abstract

Signature-based abduction aims at building hypotheses over a specified set of names, the signature, that explain an observation relative to some background knowledge. This type of abduction is useful for tasks such as diagnosis, where the vocab- ulary used for observed symptoms differs from the vocabulary expected to explain those symptoms. We present the first complete method solving signature-based abduction for observations expressed in the expressive description logic ALC, which can include TBox and ABox axioms. The method is guaranteed to compute a finite and complete set of hypotheses, and is evaluated on a set of realistic knowledge bases.

Connection-minimal Abduction in EL via Translation to FOL -- Technical Report

“…Thus it provides possible fixes in case the entailment should hold. In the DL context, depending on the shape of the observation, one distinguishes between concept abduction [8], ABox abduction [11-14, 17, 23, 28, 29, 35, 36], TBox abduction [15,38] or knowledge base abduction [19,30]. We are focusing here on TBox abduction, where the ontology and hypothesis are TBoxes and the observation is a concept inclusion (CI), i.e., a single TBox axiom.…”

“…Commonly, to avoid trivial answers, the user provides syntactic restrictions on hypotheses, such as a set of abducible axioms to pick from [12,35], a set of abducible predicates [29,30], or patterns on the shape of the solution [16]. But even with those restrictions in place, there may be many possible solutions and, to find the ones with the best explanatory potential, syntactic criteria are usually combined with minimality criteria such as subset minimality, size minimality, or semantic minimality [11].…”

“…There are not many techniques that can handle TBox abduction in EL or more expressive DLs [15,30,38]. In [15], instead of a set of abducibles, a set of justification patterns is given, in which the solutions have to fit.…”

“…While dedicated resolution calculi have been used before to solve abduction in DLs [13,30], to the best of our knowledge, the only work that relies on firstorder reasoning for DL abduction is [28]. Similar to our approach, it uses SOSresolution, but to perform ABox adbuction for the more expressive DL ALC.…”

Connection-Minimal Abduction in $$\mathcal {EL}$$ via Translation to FOL

“…Thus it provides possible fixes in case the entailment should hold. In the DL context, depending on the shape of the observation, one distinguishes between concept abduction [6], ABox abduction [7][8][9][10]12,19,24,25,30,31], TBox abduction [11,33] or knowledge base abduction [14,26]. We are focusing here on TBox abduction, where the ontology and hypothesis are TBoxes and the observation is a concept inclusion (CI), i.e., a single TBox axiom.…”