A Decidable Extension of SROIQ with Complex Role Chains and Unions
We design a decidable extension of the description logic SROIQ underlying the Web Ontology Language OWL 2. The new logic, called SR+OIQ, supports a controlled use of role axioms whose right-hand side may contain role chains or role unions. We give a tableau algorithm for checking concept satisfiability with respect to SR+OIQ ontologies and prove its soundness, completeness and termination.
This Festschrift has been put together on the occasion of Franz Baader's 60th birthday to celebrate his fundamental and highly influential scientific contributions. The 30 papers in this volume cover several scientific areas that Franz Baader has been working on during the last three decades, including description logics, term rewriting, and the combination of decision procedures. We hope that readers will enjoy the articles gathered in Franz's honour and appreciate the breadth and depth of his favourite areas of computer science.
We design temporal description logics (TDLs) suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. The logics are interpreted over the Cartesian products of object domains and the flow of time (ℤ, <), satisfying the constant domain assumption. Concept and role inclusions of the TBox hold at all moments of time (globally), and data assertions of the ABox hold at specified moments of time. To express temporal constraints of conceptual data models, the languages are equipped with flexible and rigid roles, standard future and past temporal operators on concepts, and operators “always” and “sometime” on roles. The most expressive of our TDLs (which can capture lifespan cardinalities and either qualitative or quantitative evolution constraints) turns out to be undecidable. However, by omitting some of the temporal operators on concepts/roles or by restricting the form of concept inclusions, we construct logics whose complexity ranges between NLogSpace and PSpace. These positive results are obtained by reduction to various clausal fragments of propositional temporal logic, which opens a way to employ propositional or first-order temporal provers for reasoning about temporal data models.
We investigate conjunctive query inseparability of description logic (DL) knowledge bases (KBs) with respect to a given signature, a fundamental problem for KB versioning, module extraction, forgetting and knowledge exchange. We study the data and combined complexity of deciding KB query inseparability for fragments of Horn-ALCHI, including the DLs underpinning OWL 2 QL and OWL 2 EL. While all of these DLs are P-complete for data complexity, the combined complexity ranges from P to EXPTIME and 2EXPTIME. We also resolve two major open problems for OWL 2 QL by showing that TBox query inseparability and the membership problem for universal UCQ-solutions in knowledge exchange are both EXPTIME-complete for combined complexity.
This paper further investigates the succinctness landscape of query rewriting in OWL 2 QL. We clarify the worst-case size of positive existential (PE), non-recursive Datalog (NDL), and first-order (FO) rewritings for various classes of tree-like conjunctive queries, ranging from linear queries up to bounded treewidth queries. More specifically, we establish a superpolynomial lower bound on the size of PE-rewritings that holds already for linear queries and TBoxes of depth 2. For NDL-rewritings, we show that polynomial-size rewritings always exist for tree-shaped queries with a bounded number of leaves (and arbitrary TBoxes), and for bounded treewidth queries and bounded depth TBoxes. Finally, we show that the succinctness problems concerning FO-rewritings are equivalent to well-known problems in Boolean circuit complexity. Along with known results, this yields a complete picture of the succinctness landscape for the considered classes of queries and TBoxes
Our aim is to investigate ontology-based data access over temporal data with validity time and ontologies capable of temporal conceptual modelling. To this end, we design a temporal description logic, TQL, that extends the standard ontology language OWL 2 QL, provides basic means for temporal conceptual modelling and ensures first-order rewritability of conjunctive queries for suitably defined data instances with validity time.
Full 20 pages paper:
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.