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We study the data complexity of consistent query answering (CQA) on databasesthat may violate the primary key constraints. A repair is a maximal consistentsubset of the database. For a Boolean query $q$, the problem$\mathsf{CERTAINTY}(q)$ takes a database as input, and asks whether or not eachrepair satisfies $q$. It is known that for any self-join-free Booleanconjunctive query $q$, $\mathsf{CERTAINTY}(q)$ is in $\mathbf{FO}$,$\mathbf{LSPACE}$-complete, or $\mathbf{coNP}$-complete. In particular,$\mathsf{CERTAINTY}(q)$ is in $\mathbf{FO}$ for any self-join-free Boolean pathquery $q$. In this paper, we show that if self-joins are allowed, thecomplexity of $\mathsf{CERTAINTY}(q)$ for Boolean path queries $q$ exhibits atetrachotomy between $\mathbf{FO}$, $\mathbf{NL}$-complete,$\mathbf{PTIME}$-complete, and $\mathbf{coNP}$-complete. Moreover, it isdecidable, in polynomial time in the size of the query~$q$, which of the fourcases applies.

Consistent Query Answering for Primary Keys on Path Queries