Semantics for Description Logics via Assumption-Based Argumentation: Preliminary Results

Abstract

Description Logic (DL) terminologies are collections of rules in which a class is defined in terms of a complex DL concept. Various semantics for terminologies have been proposed over the past decades. However, the tight relation with the recent W3C SHACL standard for expressing constraints over RDF graphs motivated the need to enrich terminologies with forms of commonsense reasoning. In this paper, we explore how reasoning over DL terminologies can be captured in argumentative terms, by establishing a translation into Assumption- Based Argumentation (ABA), a rule-based formalism comprising defeasible assumptions, where argumentation semantics are used to retrieve sets of jointly acceptable assumptions. We focus on the problem of graph completion, where a labeled graph is extended by assigning additional labels only to existing nodes while satisfying a given terminology. Building on the existing correspondence between logic programs and ABA, we show how a DL terminology and a labeled graph can be encoded as an ABA framework such that different completions of the graph arise from different criteria for selecting sets of assumptions. We present results for DL terminologies in 𝒜ℒ𝒞ℐ under the classical semantics, the minimal model semantics of Circumscription, and the stable model semantics of Quantified Equilibrium Logic. Furthermore, we provide preliminary results for fragments of the DL-Lite family, where the problem of graph completion is extended to allow the introduction of new domain elements, enabling full model construction.