Jean Christoph Jung

Ontology-based access to probabilistic data with OWL QL

We propose a framework for querying probabilistic instance data in the presence of an OWL2 QL ontology, arguing that the interplay of probabilities and ontologies is fruitful in many applications such as managing data that was extracted from the web. The prime inference problem is computing answer probabilities, and it can be implemented using standard probabilistic database systems. We establish a PTime vs. #P dichotomy for the data complexity of this problem by lifting a corresponding result from probabilistic databases. We also demonstrate that query rewriting (backwards chaining) is an important tool for our framework, show that non-existence of a rewriting into first-order logic implies #P-hardness, and briefly discuss approximation of answer probabilities.

Complexity of branching temporal description logics

We study branching-time temporal description logics (TDLs) based on the DLs ALC and ℇL and the temporal logics CTL and CTL*. The main contributions are algorithms for satisfiability that are more direct than existing approaches, and (mostly) tight elementary complexity bounds that range from PTIME to 2EXPTIME and 3EXPTIME. A careful use of tree automata techniques allows us to obtain transparent and uniform algorithms, avoiding to deal directly with the intricacies of CTL*.

Monodic Fragments of Probabilistic First-Order Logic

By classical results of Abadi and Halpern, validity for probabilistic first-order logic of type 2 (ProbFO) is \(\Pi^2_1\)-complete and thus not recursively enumerable, and even small fragments of ProbFO are undecidable. In temporal first-order logic, which has similar computational properties, these problems have been addressed by imposing monodicity, that is, by allowing temporal operators to be applied only to formulas with at most one free variable. In this paper, we identify a monodic fragment of ProbFO and show that it enjoys favorable computational properties. Specifically, the valid sentences of monodic ProbFO are recursively enumerable and a slight variation of Halpern’s axiom system for type-2 ProbFO on bounded domains is sound and complete for monodic ProbFO. Moreover, decidability can be obtained by restricting the FO part of monodic ProbFO to any decidable FO fragment. In some cases, which notably include the guarded fragment, our general constructions result in tight complexity bounds.

Reverse Engineering Queries in Ontology-Enriched Systems: The Case of Expressive Horn Description Logic Ontologies

We introduce the query-by-example (QBE) paradigm for query answering in the presence of ontologies. Intuitively, QBE permits non-expert users to explore the data by providing examples of the information they (do not) want, which the system then generalizes into a query. Formally, we study the following question: given a knowledge base and sets of positive and negative examples, is there a query that returns all positive but none of the negative examples? We focus on description logic knowledge bases with ontologies formulated in Horn-ALCI and (unions of) conjunctive queries. Our main contributions are characterizations, algorithms and tight complexity bounds for QBE.

Combining DL-Lite_{bool}^N with Branching Time: A gentle Marriage

We study combinations of the description logic DL-Lite_{bool}^N with the branching temporal logics CTL* and CTL. We analyse two types of combinations, both with rigid roles: (i) temporal operators are applied to concepts and to ABox assertions, and (ii) temporal operators are applied to concepts and Boolean combinations of concept inclusions and ABox assertions. For the resulting logics, we present algorithms for the satisfiability problem and (mostly tight) complexity bounds ranging from ExpTime to 3ExpTime.

Query Conservative Extensions in Horn Description Logics with Inverse Roles

We investigate the decidability and computational complexity of query conservative extensions in Horn description logics (DLs) with inverse roles. This is more challenging than without inverse roles because characterizations in terms of unbounded homomorphisms between universal models fail, blocking the standard approach to establishing decidability. We resort to a combination of automata and mosaic techniques, proving that the problem is 2EXPTIME-complete in Horn-ALCHIF (and also in Horn-ALC and in ELI). We obtain the same upper bound for deductive conservative extensions, for which we also prove a CONEXPTIME lower bound.

Conservative Extensions in Guarded and Two-Variable Fragments.

We investigate the decidability and computational complexity of (deductive) conservative extensions in fragments of first-order logic (FO), with a focus on the two-variable fragment FO

A closer look at the probabilistic description logic prob- EL

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Lightweight description logics and branching time: a troublesome marriage

and the guarded fragment GF. We prove that conservative extensions are undecidable in any FO fragment that contains FO

Lightweight temporal description logics with rigid roles and restricted TBoxes

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