Lightweight Description Logic Research Articles

Extending the description logic [formula omitted] with threshold concepts induced by concept measures

In applications of AI systems where exact definitions of the important notions of the application domain are hard to come by, the use of traditional logic-based knowledge representation languages such as Description Logics may lead to very large and unintuitive definitions, and high complexity of reasoning. To overcome this problem, we define new concept constructors that allow us to define concepts in an approximate way. To be more precise, we present a family τEL(m) of extensions of the lightweight Description Logic EL that use threshold constructors for this purpose. To define the semantics of these constructors we employ graded membership functions m, which for each individual in an interpretation and concept yield a number in the interval [0,1] expressing the degree to which the individual belongs to the concept in the interpretation. Threshold concepts C⋈t for ⋈∈{<,≤,>,≥} then collect all the individuals that belong to C with degree ⋈t. The logic τEL(m) extends EL with threshold concepts whose semantics is defined relative to a function m. To construct appropriate graded membership functions, we show how concept measures ∼ (which are graded generalizations of subsumption or equivalence between concepts) can be used to define graded membership functions m∼. Then we introduce a large class of concept measures, called simi-d, for which the logics τEL(m∼) have good algorithmic properties. Basically, we show that reasoning in τEL(m∼) is NP/coNP-complete without TBox, PSpace-complete w.r.t. acyclic TBoxes, and ExpTime-complete w.r.t. general TBoxes. The exception is the instance problem, which is already PSpace-complete without TBox w.r.t. combined complexity. While the upper bounds hold for all elements of simi-d, we could prove some of the hardness results only for a subclass of simi-d. This article considerably improves on and generalizes results we have shown in three previous conference papers and it provides detailed proofs of all our results.

Expressivity of Planning with Horn Description Logic Ontologies

State constraints in AI Planning globally restrict the legal environment states. Standard planning languages make closed-domain and closed-world assumptions. Here we address open-world state constraints formalized by planning over a description logic (DL) ontology. Previously, this combination of DL and planning has been investigated for the light-weight DL DL-Lite. Here we propose a novel compilation scheme into standard PDDL with derived predicates, which applies to more expressive DLs and is based on the rewritability of DL queries into Datalog with stratified negation. We also provide a new rewritability result for the DL Horn-ALCHOIQ, which allows us to apply our compilation scheme to quite expressive ontologies. In contrast, we show that in the slight extension Horn-SROIQ no such compilation is possible unless the weak exponential hierarchy collapses. Finally, we show that our approach can outperform previous work on existing benchmarks for planning with DL ontologies, and is feasible on new benchmarks taking advantage of more expressive ontologies.

Min-Based Conditioning of Possibilistic EL Ontology

The EL is a tractable family of lightweight description logics that underlay the OWL EL profile. It guarantees the tractability of the reasoning process, especially for concept classification. In particular, such a fragment is widely used for medical applications. This paper investigates the evolution of EL ontologies when a new piece of information that can be conflicting or attached with a confidence level reflecting its credibility or priority is available. To encode such knowledge, we propose an extension of EL description logic within the possibility theory, which provides a natural way to deal with ordinal scale reflecting ranking between pieces of knowledge. We then show how such a ranking between axioms is induced from the ontology with the presence of new information and study the evolution process at the semantic level. Finally, we propose a polynomial syntactic counterpart of the evolution process while preserving the consistency of the ontology.

On the Complexity of Consistent Query Answering in the Presence of Simple Ontologies

Consistent query answering is a standard approach for producing meaningful query answers when data is inconsistent. Recent work on consistent query answering in the presence of ontologies has shown this problem to be intractable in data complexity even for ontologies expressed in lightweight description logics. In order to better understand the source of this intractability, we investigate the complexity of consistent query answering for simple ontologies consisting only of class subsumption and class disjointness axioms. We show that for conjunctive queries with at most one quantified variable, the problem is first-order expressible; for queries with at most two quantified variables, the problem has polynomial data complexity but may not be first-order expressible; and for three quantified variables, the problem may become co-NP-hard in data complexity. For queries having at most two quantified variables, we further identify a necessary and sufficient condition for first-order expressibility. In order to be able to handle arbitrary conjunctive queries, we propose a novel inconsistency-tolerant semantics and show that under this semantics, first-order expressibility is always guaranteed. We conclude by extending our positive results to DL-Lite ontologies without inverse.

Answering Regular Path Queries Under Approximate Semantics in Lightweight Description Logics

Classical regular path queries (RPQs) can be too restrictive for some applications and answering such queries under approximate semantics to relax the query is desirable. While for answering regular path queries over graph databases under approximate semantics algorithms are available, such algorithms are scarce for the ontology-mediated setting. In this paper we extend an approach for answering RPQs over graph databases that uses weighted transducers to approximate paths from the query in two ways. The first extension is to answering approximate conjunctive 2-way regular path queries (C2RPQs) over graph databases and the second is to answering C2RPQs over ELH and DL-Lite_R ontologies. We provide results on the computational complexity of the underlying reasoning problems and devise approximate query answering algorithms.

An ASP approach for reasoning in a concept-aware multipreferential lightweight DL

AbstractIn this paper we develop a concept aware multi-preferential semantics for dealing with typicality in description logics, where preferences are associated with concepts, starting from a collection of ranked TBoxes containing defeasible concept inclusions. Preferences are combined to define a preferential interpretation in which defeasible inclusions can be evaluated. The construction of the concept-aware multipreference semantics is related to Brewka’s framework for qualitative preferences. We exploit Answer Set Programming (in particular,asprin) to achieve defeasible reasoning under the multipreference approach for the lightweight description logic ξ$\mathcal L_ \bot ^ + $.

Error-Tolerance and Error Management in Lightweight Description Logics

The construction and maintenance of ontologies is an error-prone task. As such, it is not uncommon to detect unwanted or erroneous consequences in large-scale ontologies which are already deployed in production. While waiting for a corrected version, these ontologies should still be available for use in a “safe” manner, which avoids the known errors. At the same time, the knowledge engineer in charge of producing the new version requires support to explore only the potentially problematic axioms, and reduce the number of exploration steps. In this paper, we explore the problem of deriving meaningful consequences from ontologies which contain known errors. Our work extends the ideas from inconsistency-tolerant reasoning to allow for arbitrary entailments as errors, and allows for any part of the ontology (be it the terminological elements or the facts) to be the causes of the error. Our study shows that, with a few exceptions, tasks related to this kind of reasoning are intractable in general, even for very inexpressive description logics.

Computing and Explaining Query Answers over Inconsistent DL-Lite Knowledge Bases

&#x0D; &#x0D; &#x0D; Several inconsistency-tolerant semantics have been introduced for querying inconsistent description logic knowledge bases. The first contribution of this paper is a practical approach for computing the query answers under three well-known such semantics, namely the AR, IAR and brave semantics, in the lightweight description logic DL-LiteR. We show that query answering under the intractable AR semantics can be performed efficiently by using IAR and brave semantics as tractable approximations and encoding the AR entailment problem as a propositional satisfiability (SAT) problem. The second issue tackled in this work is explaining why a tuple is a (non-)answer to a query under these semantics. We define explanations for positive and negative answers under the brave, AR and IAR semantics. We then study the computational properties of explanations in DL-LiteR. For each type of explanation, we analyze the data complexity of recognizing (preferred) explanations and deciding if a given assertion is relevant or necessary. We establish tight connections between intractable explanation problems and variants of SAT, enabling us to generate explanations by exploiting solvers for Boolean satisfaction and optimization problems. Finally, we empirically study the efficiency of our query answering and explanation framework using a benchmark we built upon the well-established LUBM benchmark.&#x0D; &#x0D; &#x0D;

The complexity of fuzzy [formula omitted] under the Łukasiewicz T-norm

Fuzzy Description Logics (DLs) are a family of knowledge representation formalisms designed to represent and reason about vague and imprecise knowledge that is inherent to many application domains. Previous work has shown that the complexity of reasoning in a fuzzy DL using finitely many truth degrees is usually not higher than that of the underlying classical DL. We show that this does not hold for fuzzy extensions of the light-weight DL EL, which is used in many biomedical ontologies, under the finitely valued Łukasiewicz semantics. More precisely, the complexity of reasoning increases from P to ExpTime, even if only one additional truth value is introduced. When adding complex role inclusions and inverse roles, the logic even becomes undecidable. Even more surprisingly, when considering the infinitely valued Łukasiewicz semantics, reasoning in fuzzy EL is undecidable.

Probabilistic implication bases in FCA and probabilistic bases of GCIs in

A probabilistic formal context is a triadic context the third dimension of which is a set of worlds equipped with a probability measure. After a formal definition of this notion, this document introduces probability of implications with respect to probabilistic formal contexts, and provides a construction for a base of implications the probabilities of which exceed a given lower threshold. A comparison between confidence and probability of implications is drawn, which yields the fact that both measures do not coincide. Furthermore, the results are extended towards the lightweight description logic with probabilistic interpretations, and a method for computing a base of general concept inclusions the probabilities of which are greater than a pre-defined lower bound is proposed. Additionally, we consider so-called probabilistic attributes over probabilistic formal contexts, and provide a method for the axiomatization of implications over probabilistic attributes.

Understanding the complexity of axiom pinpointing in lightweight description logics

Lightweight description logics are knowledge representation formalisms characterised by the low complexity of their standard reasoning tasks. They have been successfully employed for constructing large ontologies that model domain knowledge in several different practical applications. In order to maintain these ontologies, it is often necessary to detect the axioms that cause a given consequence. This task is commonly known as axiom pinpointing.In this paper, we provide a thorough analysis of the complexity of several decision, counting, and enumeration problems associated to axiom pinpointing in lightweight description logics.

The Bayesian Ontology Language $$\mathcal {BEL}$$ BEL

We introduce the new probabilistic description logic (DL) $$\mathcal {BEL} $$BEL, which extends the light-weight DL $$\mathcal {EL}$$EL with the possibility of expressing uncertainty about the validity of some knowledge. Contrary to other probabilistic DLs, $$\mathcal {BEL}$$BEL is designed to represent classical knowledge that depends on an uncertain context; that is, some of the knowledge may hold or not depending on the current situation. The probability distribution of these contexts is expressed by a Bayesian network (BN). We study different reasoning problems in $$\mathcal {BEL}$$BEL, providing tight complexity bounds for all of them. One particularly interesting property of our framework is that reasoning can be decoupled between the logical (i.e., $$\mathcal {EL}$$EL), and the probabilistic (i.e., the BN) components. We later generalize all the notions presented to introduce Bayesian extensions of arbitrary ontology languages. Using the decoupling property, we are able to provide tight complexity bounds for reasoning in the Bayesian extensions of many other DLs. We provide a detailed analysis of our formalism w.r.t. the assumptions made and compare it with the existing approaches.

OntoADR a semantic resource describing adverse drug reactions to support searching, coding, and information retrieval

IntroductionEfficient searching and coding in databases that use terminological resources requires that they support efficient data retrieval. The Medical Dictionary for Regulatory Activities (MedDRA) is a reference terminology for several countries and organizations to code adverse drug reactions (ADRs) for pharmacovigilance. Ontologies that are available in the medical domain provide several advantages such as reasoning to improve data retrieval. The field of pharmacovigilance does not yet benefit from a fully operational ontology to formally represent the MedDRA terms. Our objective was to build a semantic resource based on formal description logic to improve MedDRA term retrieval and aid the generation of on-demand custom groupings by appropriately and efficiently selecting terms: OntoADR. MethodsThe method consists of the following steps: (1) mapping between MedDRA terms and SNOMED-CT, (2) generation of semantic definitions using semi-automatic methods, (3) storage of the resource and (4) manual curation by pharmacovigilance experts. ResultsWe built a semantic resource for ADRs enabling a new type of semantics-based term search. OntoADR adds new search capabilities relative to previous approaches, overcoming the usual limitations of computation using lightweight description logic, such as the intractability of unions or negation queries, bringing it closer to user needs. Our automated approach for defining MedDRA terms enabled the association of at least one defining relationship with 67% of preferred terms. The curation work performed on our sample showed an error level of 14% for this automated approach. We tested OntoADR in practice, which allowed us to build custom groupings for several medical topics of interest. DiscussionThe methods we describe in this article could be adapted and extended to other terminologies which do not benefit from a formal semantic representation, thus enabling better data retrieval performance. Our custom groupings of MedDRA terms were used while performing signal detection, which suggests that the graphical user interface we are currently implementing to process OntoADR could be usefully integrated into specialized pharmacovigilance software that rely on MedDRA.

Explaining Inconsistency-Tolerant Query Answering over Description Logic Knowledge Bases

Several inconsistency-tolerant semantics have been introduced for querying inconsistent description logic knowledge bases. This paper addresses the problem of explaining why a tuple is a (non-)answer to a query under such semantics. We define explanations for positive and negative answers under the brave, AR and IAR semantics. We then study the computational properties of explanations in the lightweight description logic DL-Lite_R. For each type of explanation, we analyze the data complexity of recognizing (preferred) explanations and deciding if a given assertion is relevant or necessary. We establish tight connections between intractable explanation problems and variants of propositional satisfiability (SAT), enabling us to generate explanations by exploiting solvers for Boolean satisfaction and optimization problems. Finally, we empirically study the efficiency of our explanation framework using the well-established LUBM benchmark.

Regular Path Queries in Lightweight Description Logics: Complexity and Algorithms

Conjunctive regular path queries are an expressive extension of the well-known class of conjunctive queries. Such queries have been extensively studied in the (graph) database community, since they support a controlled form of recursion and enable sophisticated path navigation. Somewhat surprisingly, there has been little work aimed at using such queries in the context of description logic (DL) knowledge bases, particularly for the lightweight DLs that are considered best suited for data-intensive applications. This paper aims to bridge this gap by providing algorithms and tight complexity bounds for answering two-way conjunctive regular path queries over DL knowledge bases formulated in lightweight DLs of the DL-Lite and EL families. Our results demonstrate that in data complexity, the cost of moving to this richer query language is as low as one could wish for: the problem is NL-complete for DL-Lite and P-complete for EL. The combined complexity of query answering increases from NP- to PSpace-complete, but for two-way regular path queries (without conjunction), we show that query answering is tractable even with respect to combined complexity. Our results reveal two-way conjunctive regular path queries as a promising language for querying data enriched by ontologies formulated in DLs of the DL-Lite and EL families or the corresponding OWL 2 QL and EL profiles.

Queries with negation and inequalities over lightweight ontologies

While the problem of answering positive existential queries, in particular, conjunctive queries (CQs) and unions of CQs, over description logic ontologies has been studied extensively, there have been few attempts to analyse queries with negated atoms. Our aim is to sharpen the complexity landscape of the problem of answering CQs with negation and inequalities in lightweight description logics of the DL-Lite and EL families. We begin by considering queries with safe negation and show that there is a surprisingly significant increase in the complexity from AC0 to undecidability (even if the ontology and query are fixed and only the data is regarded as input). We also investigate the problem of answering queries with inequalities and show that answering a single CQ with one inequality over DL-Lite with role inclusions is undecidable. In the light of our undecidability results, we explore syntactic restrictions to attain efficient query answering with negated atoms. In particular, we identify a novel class of local CQs with inequalities, for which query answering over DL-Lite is decidable.

Queries with Negation and Inequalities over Lightweight Ontologies

While the problem of answering positive existential queries, in particular, conjunctive queries (CQs) and unions of CQs, over description logic ontologies has been studied extensively, there have been few attempts to analyse queries with negated atoms. Our aim is to sharpen the complexity landscape of the problem of answering CQs with negation and inequalities in lightweight description logics of the DL-Lite and &1 families. We begin by considering queries with safe negation and show that there is a surprisingly significant increase in the complexity from AC0 to undecidability (even if the ontology and query are fixed and only the data is regarded as input). We also investigate the problem of answering queries with inequalities and show that answering a single CQ with one inequality over DL-Lite with role inclusions is undecidable. In the light of our undecidability results, we explore syntactic restrictions to attain efficient query answering with negated atoms. In particular, we identify a novel class of local CQs with inequalities, for which query answering over DL-Lite is decidable.

The Logical Difference for the Lightweight Description Logic EL

We study a logic-based approach to versioning of ontologies. Under this view, ontologies provide answers to queries about some vocabulary of interest. The difference between two versions of an ontology is given by the set of queries that receive different answers. We investigate this approach for terminologies given in the description logic EL extended with role inclusions and domain and range restrictions for three distinct types of queries: subsumption, instance, and conjunctive queries. In all three cases, we present polynomial-time algorithms that decide whether two terminologies give the same answers to queries over a given vocabulary and compute a succinct representation of the difference if it is non- empty. We present an implementation, CEX2, of the developed algorithms for subsumption and instance queries and apply it to distinct versions of Snomed CT and the NCI ontology.

Tractable Extensions of the Description Logic ${\mathcal{EL}}$ with Numerical Datatypes

We consider extensions of the lightweight description logic (DL) $\mathcal{EL}$ with numerical datatypes such as naturals, integers, rationals and reals equipped with relations such as equality and inequalities. It is well-known that the main reasoning problems for such DLs are decidable in polynomial time provided that the datatypes enjoy the so-called convexity property. Unfortunately many combinations of the numerical relations violate convexity, which makes the usage of these datatypes rather limited in practice. In this paper, we make a more fine-grained complexity analysis of these DLs by considering restrictions not only on the kinds of relations that can be used in ontologies but also on their occurrences, such as allowing certain relations to appear only on the left-hand side of the axioms. To this end, we introduce a notion of safety for a numerical datatype with restrictions (NDR) which guarantees tractability, extend the $\mathcal{EL}$ reasoning algorithm to these cases, and provide a complete classification of safe NDRs for natural numbers, integers, rationals and reals.

Small is Again Beautiful in Description Logics

The Description Logic (DL) research of the last 20 years was mainly concerned with increasing the expressive power of the employed description language without losing the ability of implementing highly-optimized reasoning systems that behave well in practice, in spite of the ever increasing worst-case complexity of the underlying inference problems. OWL DL, the standard ontology language for the Semantic Web, is based on such an expressive DL for which reasoning is highly intractable. Its sublanguage OWL Lite was intended to provide a tractable version of OWL, but turned out to be only of a slightly lower worst-case complexity than OWL DL. This and other reasons have led to the development of two new families of light-weight DLs, \(\mathcal{EL}\) and DL-Lite, which recently have been proposed as profiles of OWL 2, the new version of the OWL standard. In this paper, we give an introduction to these new logics, explaining the rationales behind their design.