Revisiting Conjunctive Query Entailment for $\mathcal S$
Yazm\'in Ib\'a\~nez-Garc\'ia, Jean Christoph Jung, Vincent Michielini, Filip Murlak
TL;DR
This paper establishes the exact complexity of conjunctive query entailment over $\
Contribution
It proves the problem is 2ExpTime-complete in general and in coNExpTime under certain restrictions, clarifying previous uncertainties.
Findings
The problem is 2ExpTime-complete for unions of conjunctive queries over $\
Hardness holds with two transitive roles and Boolean queries.
The problem is in coNExpTime for rooted queries or those with at most one transitive role.
Abstract
We clarify the complexity of answering unions of conjunctive queries over knowledge bases formulated in the description logic , the extension of with transitive roles. Contrary to what existing partial results suggested, we show that the problem is in fact 2ExpTime-complete; hardness already holds in the presence of two transitive roles and for Boolean conjunctive queries. We complement this result by showing that the problem remains in coNExpTime when the input query is rooted or is restricted to use at most one transitive role (but may use arbitrarily many non-transitive roles).
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