On the uniform one-dimensional fragment

The uniform one-dimensional fragment of first-order logic, U1, is a recently introduced formalism that extends two-variable logic in a natural way to contexts with relations of all arities. We survey properties of U1 and investigate its relationship to description logics designed to accommodate higher arity relations, with particular attention given to DLR_reg. We also define a description logic version of a variant of U1 and prove a range of new results concerning the expressivity of U1 and related logics

A set-theoretical approach for ABox reasoning services (Extended Version)

In this paper we consider the most common ABox reasoning services for the description logic $\mathcal{DL}\langle \mathsf{4LQS^{R,\!\times}}\rangle(\mathbf{D})$ ($\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$, for short) and prove their decidability via a reduction to the satisfiability problem for the set-theoretic fragment \flqsr. The description logic $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$ is very expressive, as it admits various concept and role constructs, and data types, that allow one to represent rule-based languages such as SWRL. Decidability results are achieved by defining a generalization of the conjunctive query answering problem, called HOCQA (Higher Order Conjunctive Query Answering), that can be instantiated to the most wide\-spread ABox reasoning tasks. We also present a \ke\space based procedure for calculating the answer set from $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$ knowledge bases and higher order $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$ conjunctive queries, thus providing means for reasoning on several well-known ABox reasoning tasks. Our calculus extends a previously introduced \ke\space based decision procedure for the CQA problem.Comment: 27 pages. Extended version for RR 2017. arXiv admin note: text overlap with arXiv:1606.0733

Verification of Evolving Graph-structured Data under Expressive Path Constraints

Integrity constraints play a central role in databases and, among other applications, are fundamental for preserving data integrity when databases evolve as a result of operations manipulating the data. In this context, an important task is that of static verification, which consists in deciding whether a given set of constraints is preserved after the execution of a given sequence of operations, for every possible database satisfying the initial constraints. In this paper, we consider constraints over graph-structured data formulated in an expressive Description Logic (DL) that allows for regular expressions over binary relations and their inverses, generalizing many of the well-known path constraint languages proposed for semi-structured data in the last two decades. In this setting, we study the problem of static verification, for operations expressed in a simple yet flexible language built from additions and deletions of complex DL expressions. We establish undecidability of the general setting, and identify suitable restricted fragments for which we obtain tight complexity results, building on techniques developed in our previous work for simpler DLs. As a by-product, we obtain new (un)decidability results for the implication problem of path constraints, and improve previous upper bounds on the complexity of the problem

Functional Dependencies in OWL ABox

Functional Dependency (FD) has been extensively studied in database theory. Most recently there have been some works investigating the implications of extending Description Logics with functional dependencies. In particular the OWL ontology language offers the functional property property allowing simple functional dependency to be specified. As it turns out, more complex FD specified as concept constructors has been proved to lead to undecidability in the general case, which restricts its usage as part of TBOX. This paper departs from previous ones by restricting FDs applicability to instances in the ABOX. We specify FD as a new constructor, an OWL concept. FD instances are mapped to Horn clauses and evaluated against the ABOX according to user’s desired behavior. The latter allows users to determine whether FDs should be interpreted as constraints, assertions or views. Our approach gives ontology users data guarantees usually found in databases, integrated with the ontology conceptual model