# Lutz's Spoiler Technique Revisited: A Unified Approach to Worst-Case Optimal Entailment of Unions of Conjunctive Queries in Locally-Forward Description Logics

arXiv: https://arxiv.org/abs/2108.05680 · HTML: https://mlsanity.com/paper/2108.05680/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 21 references that are in the map.
- First posted on arXiv 12 Aug 2021.

## Builds on (most cited first, 4 of 4)

- [Querying the Guarded Fragment](https://mlsanity.com/paper/1309.5822/) (2013)
- [Satisfiability and Query Answering in Description Logics with Global and Local Cardinality Constraints](https://mlsanity.com/paper/2002.06072/) (2020)
- [Model Theoretic Characterisations of Description Logics](https://mlsanity.com/paper/1305.5820/) (2013)
- [The Price of Selfishness: Conjunctive Query Entailment for ALCSelf is 2ExpTime-hard](https://mlsanity.com/paper/2106.15150/) (2021)

## Abstract (arXiv)

We present a unified approach to (both finite and unrestricted) worst-case optimal entailment of (unions of) conjunctive queries (U)CQs in the wide class of "locally-forward" description logics. The main technique that we employ is a generalisation of Lutz's spoiler technique, originally developed for CQ entailment in ALCHQ. Our result closes numerous gaps present in the literature, most notably implying ExpTime-completeness of (U)CQ-querying for any superlogic of ALC contained in ALCHbregQ, and, as we believe, is abstract enough to be employed as a black-box in many new scenarios.