# Carsten Lutz's research while affiliated with University of Leipzig and other places

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## Publications (245)

We study the enumeration of answers to ontology-mediated queries when the ontology is formulated in a description logic that supports functional roles and the query is a CQ. In particular, we show that enumeration is possible with linear preprocessing and constant delay when a certain extension of the CQ (pertaining to functional roles) is acyclic...

Finding a logical formula that separates positive and negative examples given in the form of labeled data items is fundamental in applications such as concept learning, reverse engineering of database queries, generating referring expressions, and entity comparison in knowledge graphs. In this paper, we investigate the existence of a separating for...

This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating fact that this concept class lacks the polynomial-size fitting property, a property that is tacitly assumed in mu...

We study the problem to decide, given sets T1, T2 of tuple-generating dependencies (TGDs), also called existential rules, whether T2 is a conservative extension of T1. We consider two natural notions of conservative extension, one pertaining to answers to conjunctive queries over databases and one to homomorphisms between chased databases. Our main...

We study ELI queries (ELIQs) in the presence of ontologies formulated in the description logic DL-Lite. For the dialect DL-LiteH, we show that ELIQs have a frontier (set of least general generalizations) that is of polynomial size and can be computed in polynomial time. In the dialect DL-LiteF, in contrast, frontiers may be infinite. We identify a...

We study the evaluation of ontology-mediated queries (OMQs) on databases of bounded cliquewidth from the viewpoint of parameterized complexity theory. As the ontology language, we consider the description logics ALC and ALCI as well as the guarded two-variable fragment GF2 of first-order logic. Queries are atomic queries (AQs), conjunctive queries...

The fitting problem for conjunctive queries (CQs) is the problem to construct a CQ that fits a given set of labeled data examples. When a fitting CQ exists, it is in general not unique. This leads us to proposing natural refinements of the notion of a fitting CQ, such as most-general fitting CQ, most-specific fitting CQ, and unique fitting CQ. We g...

We study the evaluation of ontology-mediated queries (OMQs) on databases of bounded cliquewidth from the viewpoint of parameterized complexity theory. As the ontology language, we consider the description logics $\mathcal{ALC}$ and $\mathcal{ALCI}$ as well as the guarded two-variable fragment GF$_2$ of first-order logic. Queries are atomic queries...

We study ELI queries (ELIQs) in the presence of ontologies formulated in the description logic DL-Lite. For the dialect DL-LiteH, we show that ELIQs have a frontier (set of least general generalizations) that is of polynomial size and can be computed in polynomial time. In the dialect DL-LiteF, in contrast, frontiers may be infinite. We identify a...

We study the enumeration of answers to ontology-mediated queries (OMQs) where the ontology is a set of guarded TGDs or formulated in the description logic ELI and the query is a conjunctive query (CQ). In addition to the traditional notion of an answer, we propose and study two novel notions of partial answers that can take into account nulls gener...

We provide a fine-grained analysis of the data complexity and rewritability of ontology-mediated queries (OMQs) based on an EL ontology and a conjunctive query (CQ). Our main results are that every such OMQ is in , -complete, or -complete and that containment in coincides with rewritability into linear Datalog (whereas containment in coincides with...

We study the problem to decide, given sets T1,T2 of tuple-generating dependencies (TGDs), also called existential rules, whether T2 is a conservative extension of T1. We consider two natural notions of conservative extension, one pertaining to answers to conjunctive queries over databases and one to homomorphisms between chased databases. Our main...

We introduce and study several notions of approximation for ontology-mediated queries based on the description logics ALC and ALCI. Our approximations are of two kinds: we may (1) replace the ontology with one formulated in a tractable ontology language such as ELI or certain TGDs and (2) replace the database with one from a tractable class such as...

We study the separation of positive and negative data examples in terms of description logic concepts in the presence of an ontology. In contrast to previous work, we add a signature that specifies a subset of the symbols that can be used for separation, and we admit individual names in that signature. We consider weak and strong versions of the re...

We consider the problem to learn a concept or a query in the presence of an ontology formulated in the description logic ELr, in Angluin's framework of active learning that allows the learning algorithm to interactively query an oracle (such as a domain expert). We show that the following can be learned in polynomial time: (1) EL-concepts, (2) symm...

We study the separation of positive and negative data examples in terms of description logic concepts in the presence of an ontology. In contrast to previous work, we add a signature that specifies a subset of the symbols that can be used for separation, and we admit individual names in that signature. We consider weak and strong versions of the re...

We introduce and study several notions of approximation for ontology-mediated queries based on the description logics ALC and ALCI. Our approximations are of two kinds: we may (1) replace the ontology with one formulated in a tractable ontology language such as ELI or certain TGDs and (2) replace the database with one from a tractable class such as...

We consider the problem to learn a concept or a query in the presence of an ontology formulated in the description logic ELdr, in Angluin's framework of active learning that allows the learning algorithm to interactively query an oracle (such as a domain expert). We show that the following can be learned in polynomial time: (1) EL-concepts, (2) sym...

We study the complexity of answer counting for ontology-mediated queries and for querying under constraints, considering conjunctive queries and unions thereof (UCQs) as the query language and guarded TGDs as the ontology and constraint language, respectively. Our main result is a classification according to whether answer counting is fixed-paramet...

We study FO-rewritability of conjunctive queries in the presence of ontologies formulated in a description logic between EL and Horn-SHIF, along with related query containment problems. Apart from providing characterizations, we establish complexity results ranging from ExpTime via NExpTime to 2ExpTime, pointing out several interesting effects. In...

We investigate the decidability and computational complexity of conservative extensions and the related notions of inseparability and entailment in Horn description logics (DLs) with inverse roles. We consider both query conservative extensions, defined by requiring that the answers to all conjunctive queries are left unchanged, and deductive conse...

In ontology-based data access, multiple data sources are integrated using an ontology and mappings. In practice, this is often achieved by a bootstrapping process, that is, the ontology and mappings are first designed to support only the most important queries over the sources and then gradually extended to enable additional queries. In this paper,...

We focus on ontology-mediated queries (OMQs) based on (frontier-)guarded existential rules and (unions of) conjunctive queries, and we investigate the problem of FO-rewritability, i.e., whether an OMQ can be rewritten as a first-order query. We adopt two different approaches. The first approach employs standard two-way alternating parity tree autom...

We consider ontology-mediated queries (OMQs) based on expressive description logics of the ALC family and (unions) of conjunctive queries, studying the rewritability into OMQs based on instance queries (IQs). Our results include exact characterizations of when such a rewriting is possible and tight complexity bounds for deciding rewritability. We a...

We study the separation of positive and negative data examples in terms of description logic (DL) concepts and formulas of decidable FO fragments, in the presence of an ontology. In contrast to previous work, we add a signature that specifies a subset of the symbols from the data and ontology that can be used for separation. We consider weak and st...

Finding a logical formula that separates positive and negative examples given in the form of labeled data items is fundamental in applications such as concept learning, reverse engineering of database queries, and generating referring expressions. In this paper, we investigate the existence of a separating formula for incomplete data in the presenc...

Finding a logical formula that separates positive and negative examples given in the form of labeled data items is fundamental in applications such as concept learning, reverse engineering of database queries, and generating referring expressions. In this paper, we investigate the existence of a separating formula for incomplete data in the presenc...

We consider fragments of the description logic SHOIF extended with regular expressions on roles. Our main result is that satisfiability and finite satisfiability are decidable in two fragments SHOIF^1 and SHOIF^2, NExpTime-complete for the former and in 2NExpTime for the more expressive latter fragment. Both fragments impose restrictions on regular...

We study complete approximations of an ontology formulated in a non-Horn description logic (DL) such as ALC in a Horn DL such as EL. We provide concrete approximation schemes that are necessarily infinite and observe that in the ELU-to-EL case finite approximations tend to exist in practice and are guaranteed to exist when the source ontology is ac...

We study two forms of least general generalizations in description logic, the least common subsumer (LCS) and most specific concept (MSC). While the LCS generalizes from examples that take the form of concepts, the MSC generalizes from individuals in data. Our focus is on the complexity of existence and verification, the latter meaning to decide wh...

In ontology-mediated querying, description logic (DL) ontologies are used to enrich incomplete data with domain knowledge which results in more complete answers to queries. However, the evaluation of ontology-mediated queries (OMQs) over relational databases is computationally hard. This raises the question when OMQ evaluation is efficient, in the...

We study ontology-mediated querying in the case where ontologies are formulated in the guarded fragment of first-order logic (GF) or extensions thereof with counting and where the actual queries are (unions of) conjunctive queries. Our aim is to classify the data complexity and Datalog rewritability of query evaluation depending on the ontology O ,...

We study complete approximations of an ontology formulated in a non-Horn description logic (DL) such as $\mathcal{ALC}$ in a Horn DL such as~$\mathcal{EL}$. We provide concrete approximation schemes that are necessarily infinite and observe that in the $\mathcal{ELU}$-to-$\mathcal{EL}$ case finite approximations tend to exist in practice and are gu...

Ontology-mediated querying and querying in the presence of constraints are two key database problems where tuple-generating dependencies (TGDs) play a central role. In ontology-mediated querying, TGDs can formalize the ontology and thus derive additional facts from the given data, while in querying in the presence of constraints, they restrict the...

Learning description logic (DL) concepts from positive and negative examples given in the form of labeled data items in a KB has received significant attention in the literature. We study the fundamental question of when a separating DL concept exists and provide useful model-theoretic characterizations as well as complexity results for the associa...

We study the approximation of a description logic (DL) ontology in a less expressive DL, focusing on the case of Horn DLs. It is common to construct such approximations in an ad hoc way in practice and the resulting incompleteness is typically neither analyzed nor understood. In this paper, we show how to construct complete approximations. These ar...

This article provides an introduction to the Festschrift that has been put together on the occasion of Franz Baader’s 60th birthday to celebrate his fundamental and highly influential scientific contributions. We start with a brief and personal overview of Franz’s career, listing some important collaborators, places, and scientific milestones, and...

We provide an ultimately fine-grained analysis of the data complexity and rewritability of ontology-mediated queries (OMQs) based on an EL ontology and a conjunctive query (CQ). Our main results are that every such OMQ is in AC0, NL-complete, or PTime-complete and that containment in NL coincides with rewritability into linear Datalog (whereas cont...

We investigate the problem whether two ALC ontologies are indistinguishable (or inseparable) by means of queries in a given signature, which is fundamental for ontology engineering tasks such as ontology versioning, modularisation, update, and forgetting. We consider both knowledge base (KB) and TBox inseparability. For KBs, we give model-theoretic...

In ontology-based data access, multiple data sources are integrated using an ontology and mappings. In practice, this is often achieved by a bootstrapping process, that is, the on-tology and mappings are first designed to support only the most important queries over the sources and then gradually extended to enable additional queries. In this paper...

In the context of ontology-mediated querying with description logics (DLs), we study the data complexity of queries in which selected predicates can be closed (OMQCs). We provide a non-uniform analysis, aiming at a classification of the complexity into tractable and non-tractable for ontologies in the lightweight DLs DL-Lite and EL, and the express...

We investigate the problem whether two ALC ontologies are indistinguishable (or inseparable) by means of queries in a given signature, which is fundamental for ontology engineering tasks such as ontology versioning, modularisation, update, and forgetting. We consider both knowledge base (KB) and TBox inseparability. For KBs, we give model-theoretic...

It was recently shown by van den Broeck at al. that the symmetric weighted first-order model counting problem (WFOMC) for sentences of two-variable logic FO2 is in polynomial time, while it is #P1-complete for some FO3-sentences. We extend the result for FO2 in two independent directions: to sentences of the form ϕ∧∀x∃=1 y ψ (x, y) with ϕ...

In ontology-mediated querying with an expressive description logic L, two desirable properties of a TBox T are (1) being able to replace T with a TBox formulated in the Horn-fragment of L without affecting the answers to conjunctive queries, and (2) that every conjunctive query can be evaluated in PTime w.r.t. T. We investigate in which cases (1) a...

We focus on ontology-mediated queries (OMQs) based on (frontier-)guarded existential rules and (unions of) conjunctive queries, and we investigate the problem of FO-rewritability, i.e., whether an OMQ can be rewritten as a first-order query. We adopt two different approaches. The first approach employs standard two-way alternating parity tree autom...

We consider ontology-mediated queries (OMQs) based on expressive description logics of the ALC family and (unions) of conjunctive queries, studying the rewritability into OMQs based on instance queries (IQs). Our results include exact characterizations of when such a rewriting is possible and tight complexity bounds for deciding rewritability. We a...

It was recently shown by van den Broeck at al. that the symmetric weighted first-order model counting problem (WFOMC) for sentences of two-variable logic FO2 is in polynomial time, while it is Sharp-P_1 complete for some FO3-sentences. We extend the result for FO2 in two independent directions: to sentences of the form "phi and \forall\exists^=1 ps...

A prominent approach to implementing ontology-mediated queries (OMQs) is to rewrite into a first-order query, which is then executed using a conventional SQL database system. We consider the case where the ontology is formulated in the description logic \(\mathcal{EL}\) and the actual query is a conjunctive query and show that rewritings of such OM...

We study the problem of learning description logic (DL) ontologies in Angluin et al.'s framework of exact learning via queries. We admit membership queries ("is a given subsumption entailed by the target ontology?") and equivalence queries ("is a given ontology equivalent to the target ontology?"). We present three main results: (1) ontologies form...

We consider ontology-mediated queries (OMQs) based on an EL ontology and an atomic query (AQ), provide an ultimately fine-grained analysis of data complexity and study rewritability into linear Datalog-aiming to capture linear recursion in SQL. Our main results are that every such OMQ is in AC0, NL-complete or PTime-complete, and that containment i...

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 decidabilit...

Description logics (DLs) have a long tradition in computer science and knowledge representation, being designed so that domain knowledge can be described and so that computers can reason about this knowledge. DLs have recently gained increased importance since they form the logical basis of widely used ontology languages, in particular the web onto...

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$^2$ and the guarded fragment GF. We prove that conservative extensions are undecidable in any FO fragment that contains FO$^2$ or GF (even the three-variable fragmen...

We study the complexity of ontology-mediated querying when ontologies are formulated in the guarded fragment of first-order logic (GF). Our general aim is to classify the data complexity on the level of ontologies where query evaluation w.r.t. an ontology O is considered to be in PTime if all (unions of conjunctive) queries can be evaluated in PTim...

The question whether an ontology can safely be replaced by another, possibly simpler, one is fundamental for many ontology engineering and maintenance tasks. It underpins, for example, ontology versioning, ontology modularization, forgetting, and knowledge exchange. What ‘safe replacement’ means depends on the intended application of the ontology....

We propose a family of probabilistic description logics (DLs) that are derived in a principled way from Halpern's probabilistic first-order logic. The resulting probabilistic DLs have a two-dimensional semantics similar to temporal DLs and are well-suited for representing subjective probabilities. We carry out a detailed study of reasoning in the n...

We study rewritability of monadic disjunctive Datalog programs, (the complements of) MMSNP sentences, and ontology-mediated queries (OMQs) based on expressive description logics of the ALC family and on conjunctive queries. We show that rewritability into FO and into monadic Datalog (MDLog) are decidable, and that rewritability into Datalog is deci...

We analyze the data complexity of ontology-mediated querying where the
ontologies are formulated in a description logic (DL) of the ALC family and
queries are conjunctive queries, positive existential queries, or acyclic
conjunctive queries. Our approach is non-uniform in the sense that we aim to
understand the complexity of each single ontology in...

In ontology-based data access (OBDA), database querying is enriched with an ontology that provides domain knowledge and additional vocabulary for query formulation. We identify query emptiness and predicate emptiness as two central reasoning services in this context. Query emptiness asks whether a given query has an empty answer over all databases...

We investigate the problem whether two ALC knowledge bases are indistinguishable by queries over a given vocabulary. We give model-theoretic criteria and prove that this problem is undecidable for conjunctive queries (CQs) but decidable in 2EXPTIME for unions of rooted CQs. We also consider the problem whether two ALC TBoxes give the same answers t...

We investigate the problem whether two ALC knowledge bases are indistinguishable by queries over a given vocabulary. We give model-theoretic criteria and prove that this problem is undecid- able for conjunctive queries (CQs) but decidable in 2EXPTIME for unions of rooted CQs. We also consider the problem whether two ALC TBoxes give the same answers...

We revisit non-monotonic description logics based on circumscription (with preferences) and prove several decidability results for their satisfiability problem. In particular, we consider circumscribed description logics without the finite model property (DL-Lite\(_{\mathcal{F}}\) and \(\mathcal{ALCFI}\)) and with fixed roles (DL-Lite\(_{\mathcal{F...

We want to understand when a given TBox T in a description logic L can be rewritten into a TBox T′ in a weaker description logic L′. Two notions of rewritability are considered: model-conservative rewritability (T′ entails T and all models of T can be expanded to models of T′) and L-conservative rewritability (T′ entails T and every L-consequence o...

Ontology-based data access is concerned with querying incomplete data sources in the presence of domain-specific knowledge provided by an ontology. A central notion in this setting is that of an ontology-mediated query, which is a database query coupled with an ontology. In this paper, we study several classes of ontology-mediated queries, where th...

By classical results of Abadi and Halpern, validity for probabilistic first-order logic of type 2 (ProbFO) is Π 1 2 -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, t...

As fragments of first-order logic, Description logics (DLs) do not provide
nonmonotonic features such as defeasible inheritance and default rules. Since
many applications would benefit from the availability of such features, several
families of nonmonotonic DLs have been developed that are mostly based on
default logic and autoepistemic logic. In t...

There are several approaches to implementing query answering over instance data in the presence of an ontology that target conventional relational database systems (SQL databases) as their back-end. They all share the limitation that, for ontologies formulated in OWL2 QL or versions of the description logic DL-Lite that admit both role hierarchies...

The aim of this paper is to introduce and study model-theoretic notions of modularity in description logic and related reasoning problems. Our approach is based on a generalisation of logical equivalence that is called model-theoretic inseparability. Two TBoxes are inseparable w.r.t. a vocabulary Σ if they cannot be distinguished by the Σ-reducts o...

When answering queries in the presence of ontologies, adopting the closed world assumption for some predicates easily results in intractability. We analyze this situation on the level of individual ontologies formulated in the description logics DL-Lite and EL and show that in all cases where answering conjunctive queries (CQs) with (open and) clos...

One of the most advanced approaches to querying data in the presence of ontologies is to make use of relational database systems, rewriting the original query and the ontology into a new query that is formulated in SQL or, equivalently, in first-order logic (FO). For ontologies written in many standard description logics (DLs), however, such FO-rew...

Ontology-based data access is concerned with querying incomplete data sources
in the presence of domain-specific knowledge provided by an ontology. A central
notion in this setting is that of an ontology-mediated query, which is a
database query coupled with an ontology. In this paper, we study several
classes of ontology-mediated queries, where th...

We study polynomial time learning of description logic TBoxes in Angluin et al.'s framework of exact learning via queries.We admit entailment queries ("is a given subsumption entailed by the target TBox?") and equivalence queries ("is a given TBox equivalent to the target TBox?"), assuming that the signature and logic of the target TBox are known.W...

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 stan...

While query answering in the presence of description logic (DL) ontologies is a well-studied problem, ques-tions of static analysis such as query containment and query optimization have received less attention. In this paper, we study a rather general version of query con-tainment that, unlike the classical version, cannot be re-duced to query answ...

We consider the problem of deciding, given an instance query A(x), an EL-TBox T , and possibly an ABox signature Σ, whether A(x) is FO-rewri-table relative to T and Σ-ABoxes. Our main results are PSPACE-completeness for the case where Σ comprises all symbols and EXPTIME-completeness for the general case. We also show that the problem is in PTIME fo...

We study (i) uniform interpolation for TBoxes that are formulated in the lightweight description logic εL and (ii) εL-approximations of TBoxes formulated in more expressive languages. In both cases, we give model-theoretic characterizations based on simulations and cartesian products, and we develop algorithms that decide whether interpolants and a...

When using ontologies to access instance data, it can be useful to make a closed world assumption (CWA) for some predicates and an open world assumption (OWA) for others. The main problem with such a setup is that conjunctive query (CQ) answering becomes intractable already for inexpressive description logics such as DL-Lite and EL. We take a close...

We study branching-time temporal description logics (TDLs) based on the DLs ALC and εL 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 aut...

In description logic (DL), ABoxes are used for describing the state of affairs in an application domain. We consider the problem of updating ABoxes when the state changes, assuming that update information is described at an atomic level, i.e., in terms of possibly negated ABox assertions that involve only atomic concepts and roles. We analyze such...

Conjunctive queries play an important role as an expressive query language
for Description Logics (DLs). Although modern DLs usually provide for
transitive roles, conjunctive query answering over DL knowledge bases is only
poorly understood if transitive roles are admitted in the query. In this paper,
we consider unions of conjunctive queries over...

We study probabilistic variants of the description logic EL. For the case where probabilities apply only to concepts, we provide a careful analysis of the borderline between tractability and ExpTime-completeness. One outcome is that any probability value except zero and one leads to intractability in the presence of general TBoxes, while this is no...