Stefan Borgwardt

Temporal Query Answering in the Description Logic DL-Lite

Ontology-based data access (OBDA) generalizes query answering in relational databases. It allows to query a database by using the language of an ontology, abstracting from the actual relations of the database. For ontologies formulated in Description Logics of the DL-Lite family, OBDA can be realized by rewriting the query into a classical first-order query, e.g. an SQL query, by compiling the information of the ontology into the query. The query is then answered using classical database techniques.

Temporalizing ontology-based data access

Ontology-based data access (OBDA) generalizes query answering in databases towards deduction since (i) the fact base is not assumed to contain complete knowledge (i.e., there is no closed world assumption), and (ii) the interpretation of the predicates occurring in the queries is constrained by axioms of an ontology. OBDA has been investigated in detail for the case where the ontology is expressed by an appropriate Description Logic (DL) and the queries are conjunctive queries. Motivated by situation awareness applications, we investigate an extension of OBDA to the temporal case. As query language we consider an extension of the well-known propositional temporal logic LTL where conjunctive queries can occur in place of propositional variables, and as ontology language we use the prototypical expressive DL

The Complexity of Lattice-Based Fuzzy Description Logics

\mathcal{ALC}

Description logics over lattices with multi-valued ontologies

. For the resulting instance of temporalized OBDA, we investigate both data complexity and combined complexity of the query entailment problem.

The limits of decidability in fuzzy description logics with general concept inclusions

We study the complexity of reasoning in fuzzy description logics with semantics based on finite residuated lattices. For the logic

Temporalizing rewritable query languages over knowledge bases

\mathcal SHI

On the Decidability Status of Fuzzy

, we show that deciding satisfiability and subsumption of concepts, with or without a TBox, are ExpTime-complete problems. In