The Complexity of Answering Conjunctive and Navigational Queries over OWL 2 EL Knowledge Bases

OWL 2 EL is a popular ontology language that supports role inclusions---that is, axioms that capture compositional properties of roles. Role inclusions closely correspond to context-free grammars, which was used to show that answering conjunctive queries (CQs) over OWL 2 EL knowledge bases with unrestricted role inclusions is undecidable. However, OWL 2 EL inherits from OWL 2 DL the syntactic regularity restriction on role inclusions, which ensures that role chains implying a particular role can be described using a finite automaton (FA). This is sufficient to ensure decidability of CQ answering; however, the FAs can be worst-case exponential in size so the known approaches do not provide a tight upper complexity bound. In this paper, we solve this open problem and show that answering CQs over OWL 2 EL knowledge bases is PSPACE-complete in combined complexity (i.e., the complexity measured in the total size of the input). To this end, we use a novel encoding of regular role inclusions using bounded-stack pushdown automata---that is, FAs extended with a stack of bounded size. Apart from theoretical interest, our encoding can be used in practical tableau algorithms to avoid the exponential blowup due to role inclusions. In addition, we sharpen the lower complexity bound and show that the problem is PSPACE-hard even if we consider only role inclusions as part of the input (i.e., the query and all other parts of the knowledge base are fixed). Finally, we turn our attention to navigational queries over OWL 2 EL knowledge bases, and we show that answering positive, converse-free conjunctive graph XPath queries is PSPACE-complete as well; this is interesting since allowing the converse operator in queries is known to make the problem EXPTIME-hard. Thus, in this paper we present several important contributions to the landscape of the complexity of answering expressive queries over description logic knowledge bases.

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ASP for minimal entailment in a rational extension of SROEL

Theory and Practice of Logic Programming ◽

10.1017/s1471068416000399 ◽

2016 ◽

Vol 16 (5-6) ◽

pp. 738-754 ◽

Cited By ~ 2

Author(s):

LAURA GIORDANO ◽

DANIELE THESEIDER DUPRÉ

Keyword(s):

Description Logic ◽

Polynomial Complexity ◽

Answer Set Programming ◽

Low Complexity ◽

Knowledge Bases ◽

Ontology Language ◽

Rational Extension ◽

Small Model ◽

Answer Sets ◽

Answer Set

AbstractIn this paper we exploit Answer Set Programming (ASP) for reasoning in a rational extensionSROEL(⊓,×)RTof the low complexity description logicSROEL(⊓, ×), which underlies the OWL EL ontology language. In the extended language, a typicality operatorTis allowed to define conceptsT(C) (typicalC's) under a rational semantics. It has been proven that instance checking under rational entailment has a polynomial complexity. To strengthen rational entailment, in this paper we consider a minimal model semantics. We show that, for arbitrarySROEL(⊓,×)RTknowledge bases, instance checking under minimal entailment is ΠP2-complete. Relying on a Small Model result, where models correspond to answer sets of a suitable ASP encoding, we exploit Answer Set Preferences (and, in particular, theasprinframework) for reasoning under minimal entailment.

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ByNowLife: A Novel Framework for OWL and Bayesian Network Integration

Information ◽

10.3390/info10030095 ◽

2019 ◽

Vol 10 (3) ◽

pp. 95

Author(s):

Foni Setiawan ◽

Eko Budiardjo ◽

Wahyu Wibowo

Keyword(s):

Bayesian Network ◽

Knowledge Base ◽

Structural Adjustment ◽

Description Logic ◽

Probabilistic Reasoning ◽

Knowledge Bases ◽

Third Party ◽

Probabilistic Information ◽

Ontology Language ◽

Novel Approach

An ontology-based system can currently logically reason through the Web Ontology Language Description Logic (OWL DL). To perform probabilistic reasoning, the system must use a separate knowledge base, separate processing, or third-party applications. Previous studies mainly focus on how to represent probabilistic information in ontologies and perform reasoning through them. These approaches are not suitable for systems that already have running ontologies and Bayesian network (BN) knowledge bases because users must rewrite the probabilistic information contained in a BN into an ontology. We present a framework called ByNowLife, which is a novel approach for integrating BN with OWL by providing an interface for retrieving probabilistic information through SPARQL queries. ByNowLife catalyzes the integration process by transforming logical information contained in an ontology into a BN and probabilistic information contained in a BN into an ontology. This produces a system with a complete knowledge base. Using ByNowLife, a system that already has separate ontologies and BN knowledge bases can integrate them into a single knowledge base and perform both logical and probabilistic reasoning through it. The integration not only facilitates the unity of reasoning but also has several other advantages, such as ontology enrichment and BN structural adjustment through structural and parameter learning.

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Enriched Meanings

10.1093/oso/9780198847854.001.0001 ◽

2020 ◽

Author(s):

Ash Asudeh ◽

Gianluca Giorgolo

Keyword(s):

Cognitive Science ◽

Programming Languages ◽

Category Theory ◽

Worst Case ◽

Disciplinary Boundaries ◽

Semantics Of Programming Languages ◽

Basic Meaning ◽

Language Interpretation ◽

Major Branch ◽

Compositional Properties

This book presents a theory of enriched meanings for natural language interpretation. Certain expressions that exhibit complex effects at the semantics/pragmatics boundary live in an enriched meaning space while others live in a more basic meaning space. These basic meanings are mapped to enriched meanings just when required compositionally, which avoids generalizing meanings to the worst case. The theory is captured formally using monads, a concept from category theory. Monads are also prominent in functional programming and have been successfully used in the semantics of programming languages to characterize certain classes of computation. They are used here to model certain challenging linguistic computations at the semantics/pragmatics boundary. Part I presents some background on the semantics/pragmatics boundary, informally presents the theory of enriched meanings, reviews the linguistic phenomena of interest, and provides the necessary background on category theory and monads. Part II provides novel compositional analyses of the following phenomena: conventional implicature, substitution puzzles, and conjunction fallacies. Part III explores the prospects of combining monads, with particular reference to these three cases. The authors show that the compositional properties of monads model linguistic intuitions about these cases particularly well. The book is an interdisciplinary contribution to Cognitive Science: These phenomena cross not just the boundary between semantics and pragmatics, but also disciplinary boundaries between Linguistics, Philosophy and Psychology, three of the major branches of Cognitive Science, and are here analyzed with techniques that are prominent in Computer Science, a fourth major branch. A number of exercises are provided to aid understanding, as well as a set of computational tools (available at the book's website), which also allow readers to develop their own analyses of enriched meanings.

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An Improved Set-based Reasoner for the Description Logic 𝒟ℒD4,×†

Fundamenta Informaticae ◽

10.3233/fi-2021-2009 ◽

2021 ◽

Vol 178 (4) ◽

pp. 315-346

Author(s):

Domenico Cantone ◽

Marianna Nicolosi-Asmundo ◽

Daniele Francesco Santamaria

Keyword(s):

Semantic Web ◽

Set Theory ◽

Description Logic ◽

Knowledge Bases ◽

Query Answering ◽

Conjunctive Query ◽

Classification Problems ◽

Previous Version ◽

Decidable Fragment ◽

Stratified Set

We present a KE-tableau-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic 𝒟ℒ〈4LQSR,×〉(D) (𝒟ℒD4,×, for short). Our application solves the main TBox and ABox reasoning problems for 𝒟ℒD4,×. In particular, it solves the consistency and the classification problems for 𝒟ℒD4,×-knowledge bases represented in set-theoretic terms, and a generalization of the Conjunctive Query Answering problem in which conjunctive queries with variables of three sorts are admitted. The reasoner, which extends and improves a previous version, is implemented in C++. It supports 𝒟ℒD4,×-knowledge bases serialized in the OWL/XML format and it admits also rules expressed in SWRL (Semantic Web Rule Language).

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Acyclicity Notions for Existential Rules and Their Application to Query Answering in Ontologies

Journal of Artificial Intelligence Research ◽

10.1613/jair.3949 ◽

2013 ◽

Vol 47 ◽

pp. 741-808 ◽

Cited By ~ 30

Author(s):

B. Cuenca Grau ◽

I. Horrocks ◽

M. Krötzsch ◽

C. Kupke ◽

D. Magka ◽

...

Keyword(s):

Knowledge Representation ◽

Sufficient Conditions ◽

Query Answering ◽

Conjunctive Queries ◽

Practical Solution ◽

Ontology Language ◽

Lower Complexity ◽

The Given ◽

Theoretical Side

Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a prominent problem in knowledge representation and databases. This problem can be solved using the chase algorithm, which extends the given set of facts with fresh facts in order to satisfy the rules. If the chase terminates, then CQs can be evaluated directly in the resulting set of facts. The chase, however, does not terminate necessarily, and checking whether the chase terminates on a given set of rules and facts is undecidable. Numerous acyclicity notions were proposed as sufficient conditions for chase termination. In this paper, we present two new acyclicity notions called model-faithful acyclicity (MFA) and model-summarising acyclicity (MSA). Furthermore, we investigate the landscape of the known acyclicity notions and establish a complete taxonomy of all notions known to us. Finally, we show that MFA and MSA generalise most of these notions. Existential rules are closely related to the Horn fragments of the OWL 2 ontology language; furthermore, several prominent OWL 2 reasoners implement CQ answering by using the chase to materialise all relevant facts. In order to avoid termination problems, many of these systems handle only the OWL 2 RL profile of OWL 2; furthermore, some systems go beyond OWL 2 RL, but without any termination guarantees. In this paper we also investigate whether various acyclicity notions can provide a principled and practical solution to these problems. On the theoretical side, we show that query answering for acyclic ontologies is of lower complexity than for general ontologies. On the practical side, we show that many of the commonly used OWL 2 ontologies are MSA, and that the number of facts obtained by materialisation is not too large. Our results thus suggest that principled development of materialisation-based OWL 2 reasoners is practically feasible.

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Building an OWL ontology with Xper3

Biodiversity Information Science and Standards ◽

10.3897/biss.2.25614 ◽

2018 ◽

Vol 2 ◽

pp. e25614 ◽

Cited By ~ 1

Author(s):

Florian Pellen ◽

Sylvain Bouquin ◽

Isabelle Mougenot ◽

Régine Vignes-Lebbe

Keyword(s):

Semantic Web ◽

Knowledge Base ◽

Expressive Power ◽

Knowledge Bases ◽

User Friendliness ◽

Standard Format ◽

Ontology Language ◽

Closed World ◽

Web Standards ◽

Description Framework

Xper3 (Vignes Lebbe et al. 2016) is a collaborative knowledge base publishing platform that, since its launch in november 2013, has been adopted by over 2 thousand users (Pinel et al. 2017). This is mainly due to its user friendly interface and the simplicity of its data model. The data are stored in MySQL Relational DBs, but the exchange format uses the TDWG standard format SDD (Structured Descriptive DataHagedorn et al. 2005). However, each Xper3 knowledge base is a closed world that the author(s) may or may not share with the scientific community or the public via publishing content and/or identification key (Kopfstein 2016). The explicit taxonomic, geographic and phenotypic limits of a knowledge base are not always well defined in the metadata fields. Conversely terminology vocabularies, such as Phenotype and Trait Ontology PATO and the Plant Ontology PO, and software to edit them, such as Protégé and Phenoscape, are essential in the semantic web, but difficult to handle for biologist without computer skills. These ontologies constitute open worlds, and are expressed themselves by RDF triples (Resource Description Framework). Protégé offers vizualisation and reasoning capabilities for these ontologies (Gennari et al. 2003, Musen 2015). Our challenge is to combine the user friendliness of Xper3 with the expressive power of OWL (Web Ontology Language), the W3C standard for building ontologies. We therefore focused on analyzing the representation of the same taxonomic contents under Xper3 and under different models in OWL. After this critical analysis, we chose a description model that allows automatic export of SDD to OWL and can be easily enriched. We will present the results obtained and their validation on two knowledge bases, one on parasitic crustaceans (Sacculina) and the second on current ferns and fossils (Corvez and Grand 2014). The evolution of the Xper3 platform and the perspectives offered by this link with semantic web standards will be discussed.

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Lower complexity bounds for lifted inference

Theory and Practice of Logic Programming ◽

10.1017/s1471068413000707 ◽

2014 ◽

Vol 15 (2) ◽

pp. 246-263 ◽

Cited By ~ 4

Author(s):

MANFRED JAEGER

Keyword(s):

Knowledge Bases ◽

Modeling Languages ◽

Complexity Bounds ◽

Lifted Inference ◽

Probabilistic Relational Models ◽

Lower Complexity ◽

Logical Modeling ◽

Inference Techniques ◽

And Function ◽

Lower Complexity Bounds

AbstractOne of the big challenges in the development of probabilistic relational (or probabilistic logical) modeling and learning frameworks is the design of inference techniques that operate on the level of the abstract model representation language, rather than on the level of ground, propositional instances of the model. Numerous approaches for such “lifted inference” techniques have been proposed. While it has been demonstrated that these techniques will lead to significantly more efficient inference on some specific models, there are only very recent and still quite restricted results that show the feasibility of lifted inference on certain syntactically defined classes of models. Lower complexity bounds that imply some limitations for the feasibility of lifted inference on more expressive model classes were established earlier in Jaeger (2000; Jaeger, M. 2000. On the complexity of inference about probabilistic relational models. Artificial Intelligence 117, 297–308). However, it is not immediate that these results also apply to the type of modeling languages that currently receive the most attention, i.e., weighted, quantifier-free formulas. In this paper we extend these earlier results, and show that under the assumption that NETIME≠ETIME, there is no polynomial lifted inference algorithm for knowledge bases of weighted, quantifier-, and function-free formulas. Further strengthening earlier results, this is also shown to hold for approximate inference and for knowledge bases not containing the equality predicate.

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Semantic Web Rule Languages for Geospatial Ontologies

Web Technologies ◽

10.4018/978-1-60566-982-3.ch035 ◽

2011 ◽

pp. 648-669

Author(s):

Philip D. Smart ◽

Alia I. Abdelmoty ◽

Baher A. El-Geresy ◽

Christopher B. Jones

Keyword(s):

Semantic Web ◽

Description Logic ◽

Continuous Process ◽

Geographical Information ◽

Ontology Language ◽

Rule Languages ◽

Sample Application ◽

Representation Language ◽

Representational Approach ◽

Geospatial Ontologies

Geospatial ontologies have a key role to play in the development of the geospatial-Semantic Web, with regard to facilitating the search for geographical information and resources. They normally hold large volumes of geographic information and undergo a continuous process of revision and update. Limitations of the OWL ontology representation language for supporting geospatial domains are discussed and an integrated rule and ontology language is recognized as needed to support the representation and reasoning requirements in this domain. A survey of the current approaches to integrating ontologies and rules is presented and a new framework is proposed that is based on and extends Description Logic Programs. A hybrid representational approach is adopted where the logical component of the framework is used to represent geographical concepts and spatial rules and an external computational geometry processor is used for storing and manipulating the associated geometric data. A sample application is used to demonstrate the proposed language and engine and how they address the identified challenges.

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Reasoning on the Semantic Web

Semantic Web Services ◽

10.4018/978-1-59904-045-5.ch006 ◽

2011 ◽

pp. 110-133

Author(s):

R. Brussee

Keyword(s):

Real World ◽

Description Logic ◽

World Knowledge ◽

Closed World Assumption ◽

Sharp Distinction ◽

Ontology Language ◽

Closed World ◽

Present Information ◽

Logical Modeling ◽

Case Reasoning

We describe reasoning as the process needed for using logic. Efficiently performing this process is a prerequisite for using logic to present information in a declarative way and to construct models of reality. In particular we describe description logic and the owl ontology language and explain that in this case reasoning amounts to graph completion operations that can be performed by a computer program. We give an extended example, modeling a building with wireless routers and explain how such a model can help in determining the location of resources. We emphasize how different assumptions on the way routers and buildings work are formalized and made explicit in our logical modeling, and explain the sharp distinction between knowing some facts and knowing all facts (open vs. closed world assumption). This should be helpful when using ontologies in applications needing incomplete real world knowledge.

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