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 conservative extensions, which require that the entailed concept inclusions, role inclusions, and functionality assertions do not change. Upper bounds for query conservative extensions are particularly challenging because characterizations in terms of unbounded homomorphisms between universal models, which are the foundation of the standard approach to establishing decidability, fail in the presence of inverse roles. We resort to a characterization that carefully mixes unbounded and bounded homomorphisms and enables a decision procedure that combines tree automata and a mosaic technique. Our main results are that query conservative extensions are 2ExpTime-complete in all DLs between ELI and Horn-ALCHIF and between Horn-ALC and Horn-ALCHIF, and that deductive conservative extensions are 2ExpTime-complete in all DLs between ELI and ELHIF_bot. The same results hold for inseparability and entailment.

With the growth of ontologies used in diverse application areas, the need for module extraction and modularisation techniques has risen. The notion of the modular structure of an ontology, which comprises a suitable set of base modules together with their logical dependencies, has the potential to help users and developers in comprehending, sharing, and maintaining an ontology. We have developed a new modular structure, called atomic decomposition (AD), which is based on modules that provide strong logical properties, such as locality-based modules. In this article, we present the theoretical foundations of AD, review its logical and computational properties, discuss its suitability as a modular structure, and report on an experimental evaluation of AD. In addition, we discuss the concept of a modular structure in ontology engineering and provide a survey of existing decomposition approaches.

Originating from Allen's Interval Algebra, composition-based reasoning has been widely acknowledged as the most popular reasoning technique in qualitative spatial and temporal reasoning. Given a qualitative calculus (i.e. a relation model), the first thing we should do is to establish its composition table (CT). In the past three decades, such work is usually done manually. This is undesirable and error-prone, given that the calculus may contain tens or hundreds of basic relations. Computing the correct CT has been identified by Tony Cohn as a challenge for computer scientists in 1995. This paper addresses this problem and introduces a semi-automatic method to compute the CT by randomly generating triples of elements. For several important qualitative calculi, our method can establish the correct CT in a reasonable short time. This is illustrated by applications to the Interval Algebra, the Region Connection Calculus RCC-8, the INDU calculus, and the Oriented Point Relation Algebras. Our method can also be used to generate CTs for customised qualitative calculi defined on restricted domains.

The unary negation fragment of first-order logic (UNFO) has recently been proposed as a generalization of modal logic that shares many of its good computational and model-theoretic properties. It is attractive from the perspective of database theory because it can express conjunctive queries (CQs) and ontologies formulated in many description logics (DLs). Both are relevant for ontology-mediated querying and, in fact, CQ evaluation under UNFO ontologies (and thus also under DL ontologies) can be `expressed' in UNFO as a satisfiability problem. In this paper, we consider the natural extension of UNFO with regular expressions on binary relations. The resulting logic UNFOreg can express (unions of) conjunctive two-way regular path queries (C2RPQs) and ontologies formulated in DLs that include transitive roles and regular expressions on roles. Our main results are that evaluating C2RPQs under UNFOreg ontologies is decidable, 2ExpTime-complete in combined complexity, and coNP-complete in data complexity, and that satisfiability in UNFOreg is 2ExpTime-complete, thus not harder than in UNFO.

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 fragment thereof), and that they are decidable and 2\ExpTime-complete in the intersection GF$^2$ of FO$^2$ and GF.

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.

The OWL 2 profile OWL 2 QL, based on the DL-Lite family of description logics, is emerging as a major language for developing new ontologies and approximating the existing ones. Its main application is ontology-based data access, where ontologies are used to provide background knowledge for answering queries over data. We investigate the corresponding notion of query inseparability (or equivalence) for OWL 2 QL ontologies and show that deciding query inseparability is PSPACE-hard and in EXPTIME. We give polynomial time (incomplete) algorithms and demonstrate by experiments that they can be used for practical module extraction.

Extracting a subset of a given ontology that cap-tures all the ontology’s knowledge about a specified set of terms is a well-understood task. This task can be based, for instance, on locality-based mod-ules. However, a single module does not allow us to understand neither topicality, connectedness, struc-ture, or superfluous parts of an ontology, nor agree-ment between actual and intended modeling. The strong logical properties of locality-based modules suggest that the family of all such mod-ules of an ontology can support comprehension of the ontology as a whole. However, extracting that family is not feasible, since the number of locality-based modules of an ontology can be exponential w.r.t. its size. In this paper we report on a new approach that en-ables us to efficiently extract a polynomial repres-entation of the family of all locality-based modules of an ontology. We also describe the fundamental algorithm to pursue this task, and report on experi-ments carried out and results obtained. 1

OBJECTIVES: (a) To determine the extent and range of errors and issues in the Systematised Nomenclature of Medicine-Clinical Terms (SNOMED CT) hierarchies as they affect two practical projects. (b) To determine the origin of issues raised and propose methods to address them. METHODS: The hierarchies for concepts in the Core Problem List Subset published by the Unified Medical Language System were examined for their appropriateness in two applications. Anomalies were traced to their source to determine whether they were simple local errors, systematic inferences propagated by SNOMED's classification process, or the result of problems with SNOMED's schemas. Conclusions were confirmed by showing that altering the root cause and reclassifying had the intended effects, and not others. MAIN RESULTS: Major problems were encountered, involving concepts central to medicine including myocardial infarction, diabetes, and hypertension. Most of the issues raised were systematic. Some exposed fundamental errors in SNOMED's schemas, particularly with regards to anatomy. In many cases, the root cause could only be identified and corrected with the aid of a classifier. LIMITATIONS: This is a preliminary 'experiment of opportunity.' The results are not exhaustive; nor is consensus on all points definitive. CONCLUSIONS: The SNOMED CT hierarchies cannot be relied upon in their present state in our applications. However, systematic quality assurance and correction are possible and practical but require sound techniques analogous to software engineering and combined lexical and semantic techniques. Until this is done, anyone using SNOMED codes should exercise caution. Errors in the hierarchies, or attempts to compensate for them, are likely to compromise interoperability and meaningful use.

In a seminal paper from 1985, Sistla and Clarke showed that the model-checking problem for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If in contrast, the set of propositional operators is restricted, the complexity may decrease. This article systematically studies the model-checking problem for LTL formulae over restricted sets of propositional and temporal operators. For almost all combinations of temporal and propositional operators, we determine whether the model-checking problem is tractable (in PTIME) or intractable (NP-hard). We then focus on the tractable cases, showing that they all are NL-complete or even logspace solvable. This leads to a surprising gap in complexity between tractable and intractable cases. It is worth noting that our analysis covers an infinite set of problems, since there are infinitely many sets of propositional operators.

The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of negations---restrictions already studied for LTL by Sistla and Clarke (1985) and Markey (2004).For all these fragments, except for the trivial case without any temporal operator, we systematically prove model checking to be either inherently sequential (P-complete) or very efficiently parallelizable (LOGCFL-complete). For most fragments, however, model checking for CTL is already P-complete. Hence our results indicate that in most applications, approaching CTL model checking by parallelism will not result in the desired speed up. We also completely determine the complexity of the model checking problem for all fragments of the extensions ECTL, CTL+, and ECTL+.

In a seminal paper from 1985, Sistla and Clarke showed that satisfiability for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If, in contrast, the set of propositional operators is restricted, the complexity may decrease. This paper undertakes a systematic study of satisfiability for LTL formulae over restricted sets of propositional and temporal operators. Since every propositional operator corresponds to a Boolean function, there exist infinitely many propositional operators. In order to systematically cover all possible sets of them, we use Post's lattice. With its help, we determine the computational complexity of LTL satisfiability for all combinations of temporal operators and all but two classes of propositional functions. Each of these infinitely many problems is shown to be either PSPACE-complete, NP-complete, or in P.