Combining Spatial and Temporal Logics: Expressiveness vs. Complexity

In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PTL, the spatial logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and computational realisability within the hierarchy. We demonstrate how different combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out of components that are at most NP- or PSPACE-complete

Query rewriting under linear EL knowledge bases

With the adoption of the recent SPARQL 1.1 standard, RDF databases are capable of directly answering more expressive queries than simple conjunctive queries. In this paper we exploit such capabilities to answer conjunctive queries (CQs) under ontologies expressed in the description logic called linear EL-lin, a restricted form of EL. In particular, we show a query answering algorithm that rewrites a given CQ into a conjunctive regular path query (CRPQ) which, evaluated on the given instance, returns the correct answer. Our technique is based on the representation of infinite unions of CQs by non-deterministic finite-state automata. Our results achieve optimal data complexity, as well as producing rewritings straightforwardly implementable in SPARQL 1.1

Circuit Complexity Meets Ontology-Based Data Access

Ontology-based data access is an approach to organizing access to a database augmented with a logical theory. In this approach query answering proceeds through a reformulation of a given query into a new one which can be answered without any use of theory. Thus the problem reduces to the standard database setting. However, the size of the query may increase substantially during the reformulation. In this survey we review a recently developed framework on proving lower and upper bounds on the size of this reformulation by employing methods and results from Boolean circuit complexity.Comment: To appear in proceedings of CSR 2015, LNCS 9139, Springe

Ontology-based data access: a survey

We present the framework of ontology-based data access, a semantic paradigm for providing a convenient and user-friendly access to data repositories, which has been actively developed and studied in the past decade. Focusing on relational data sources, we discuss the main ingredients of ontology-based data access, key theoretical results, techniques, applications and future challenges

Answering SPARQL queries over databases under OWL 2 QL entailment regime

We present an extension of the ontology-based data access platform Ontop that supports answering SPARQL queries under the OWL 2 QL direct semantics entailment regime for data instances stored in relational databases. On the theoretical side, we show how any input SPARQL query, OWL 2 QL ontology and R2RML mappings can be rewritten to an equivalent SQL query solely over the data. On the practical side, we present initial experimental results demonstrating that by applying the Ontop technologies—the tree-witness query rewriting, T-mappings compiling R2RML mappings with ontology hierarchies, and T-mapping optimisations using SQL expressivity and database integrity constraints—the system produces scalable SQL queries

Horn fragments of the Halpern-Shoham Interval Temporal Logic

We investigate the satisfiability problem for Horn fragments of the Halpern-Shoham interval temporal logic depending on the type (box or diamond) of the interval modal operators, the type of the underlying linear order (discrete or dense), and the type of semantics for the interval relations (reflexive or irreflexive). For example, we show that satisfiability of Horn formulas with diamonds is undecidable for any type of linear orders and semantics. On the contrary, satisfiability of Horn formulas with boxes is tractable over both discrete and dense orders under the reflexive semantics and over dense orders under the irreflexive semantics but becomes undecidable over discrete orders under the irreflexive semantics. Satisfiability of binary Horn formulas with both boxes and diamonds is always undecidable under the irreflexive semantics