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Exact query reformulation over databases with first-order and description logics ontologies

We study a general framework for query rewriting in the presence of an arbitrary first-order logic ontology over a database signature. The framework supports deciding the existence of a safe-range first-order equivalent reformulation of a query in terms of the database signature, and if so, it provides an effective approach to construct the reformulation based on interpolation using standard theorem proving techniques (e.g., tableau). Since the reformulation is a safe-range formula, it is effectively executable as an SQL query. At the end, we present a non-trivial application of the framework with ontologies in the very expressive ALCHOIQ description logic, by providing effective means to compute safe-range first-order exact reformulations of queries.

Exact query reformulation with first-order ontologies and databases

We study a general framework for query rewriting in the presence of an arbitrary first-order logic ontology over a database signature. The framework supports deciding the existence of a safe-range first-order equivalent reformulation of a query in terms of the database signature, and if so, it provides an effective approach to construct the reformulation based on interpolation using standard theorem proving techniques (e.g., tableau). Since the reformulation is a safe-range formula, it is effectively executable as an SQL query. At the end, we present an application of the framework with

The definability abduction problem for data exchange

\mathcal{SHOQ}

Unique Solutions in Data Exchange

ontologies.

Getting unique solution in data exchange

Data exchange is the problem of transforming data structured according to a source schema into data structured according to a target schema, via a mapping specified by means of rules in the form of source-to-targettuplegeneratingdependencies --- rules whose body is a conjunction of atoms over the source schema and the head is a conjunction of atoms over the target schema, with possibly existential variables in the head. With this formalization, given a fixed source database, there might be more than one target databases satisfying a given mapping. That is, the target database is actually an incompletedatabase represented by a set of possible databases. Therefore, the problem of query answering the target data is inherently complex for general (non-positive) relational or aggregate queries.

The Combined Complexity of Reasoning with Closed Predicates in Description Logics.

Data exchange is the problem of transforming data structured according to a source schema into data structured according to a target schema, via a mapping specified by rules in the form of source-to-target tuple generating dependencies. In this context, given a source instance and a mapping, there might be more than one valid target instance that satisfies the mapping. This issue contradicts the main goal of exchanging data, namely to have a materialised target instance that can be used to answer queries over the target schema without reference to the original source instance. In this paper we introduce and solve the novel problem of definability abduction, which aims at finding extensions to the initial schema mappings to guarantee the uniqueness of the materialised target instance. We consider several semantic criteria to select reasonable extensions and provide provably sound and complete algorithms to generate these additions. We also do a complexity analysis in different data exchange settings, also with source and target dependencies.

Closed predicates in description logics: results on combined complexity

A schema mapping is a high-level specification in which the relationship between two database schemas is described. In data exchange, schema mappings are one-way mappings that describe which data can be brought from source data to target data. Therefore, given a source instance and a mapping, there might be more than one valid target instance. This fact causes many problems in query answering over target data for non-conjunctive queries. To make query answering feasible for all queries, we focus on a methodology for extending the original schema mapping to guarantee the uniqueness of target instance corresponding to a source instance. To this end, we introduce a theoretical framework where the problem is transformed to an abduction problem, namely, definability abduction. We apply the framework to relational data exchange setting and solve the problem by pointing out minimal solutions according to a specific semantic minimality criterion.