Queries with Guarded Negation (full version)

A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical algorithms in the case of unions of conjunctive queries, but become difficult or even undecidable when queries are allowed to contain negation. Inspired by recent results in finite model theory, we consider a restricted form of negation, guarded negation. We introduce a fragment of SQL, called GN-SQL, as well as a fragment of Datalog with stratified negation, called GN-Datalog, that allow only guarded negation, and we show that these query languages are computationally well behaved, in terms of testing query containment, query evaluation, open-world query answering, and boundedness. GN-SQL and GN-Datalog subsume a number of well known query languages and constraint languages, such as unions of conjunctive queries, monadic Datalog, and frontier-guarded tgds. In addition, an analysis of standard benchmark workloads shows that most usage of negation in SQL in practice is guarded negation

Conjunctive Query Answering for the Description Logic SHIQ

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, conjunctive query answering over DL knowledge bases is only poorly understood if transitive roles are admitted in the query. In this paper, we consider unions of conjunctive queries over knowledge bases formulated in the prominent DL SHIQ and allow transitive roles in both the query and the knowledge base. We show decidability of query answering in this setting and establish two tight complexity bounds: regarding combined complexity, we prove that there is a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query, which is optimal. Regarding data complexity, we prove containment in co-NP

Ronciling Differences

In this paper we study a problem motivated by the management of changes in databases. It turns out that several such change scenarios, e.g., the separately studied problems of view maintenance (propagation of data changes) and view adaptation (propagation of view definition changes) can be unified as instances of query reformulation using views provided that support for the relational difference operator exists in the context of query reformulation. Exact query reformulation using views in positive relational languages is well understood, and has a variety of applications in query optimization and data sharing. Unfortunately, most questions about queries become undecidable in the presence of difference (or negation), whether we use the foundational set semantics or the more practical bag semantics. We present a new way of managing this difficulty by defining a novel semantics, Z- relations, where tuples are annotated with positive or negative integers. Z-relations conveniently represent data, insertions, and deletions in a uniform way, and can apply deletions with the union operator (deletions are tuples with negative counts). We show that under Z-semantics relational algebra (R A) queries have a normal form consisting of a single difference of positive queries, and this leads to the decidability of their equivalence.We provide a sound and complete algorithm for reformulating R A queries, including queries with difference, over Z-relations. Additionally, we show how to support standard view maintenanc

Eliminating Recursion from Monadic Datalog Programs on Trees

We study the problem of eliminating recursion from monadic datalog programs on trees with an infinite set of labels. We show that the boundedness problem, i.e., determining whether a datalog program is equivalent to some nonrecursive one is undecidable but the decidability is regained if the descendant relation is disallowed. Under similar restrictions we obtain decidability of the problem of equivalence to a given nonrecursive program. We investigate the connection between these two problems in more detail