scholarly journals Rewriting the Description Logic ALCHIQ to Disjunctive Existential Rules

2020 ◽  
Author(s):  
David Carral ◽  
Markus Krötzsch
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Data Intensive ◽  
Polynomial Size ◽  
Bounded Size

Especially in data-intensive settings, a promising reasoning approach for description logics (DLs) is to rewrite DL theories into sets of rules. Although many such approaches have been considered in the literature, there are still various relevant DLs for which no small rewriting (of polynomial size) is known. We therefore develop small rewritings for the DL \ALCHIQ -- featuring disjunction, number restrictions, and inverse roles -- to disjunctive Datalog. By admitting existential quantifiers in rule heads, we can improve this result to yield only rules of bounded size, a property that is common to all rewritings that were implemented in practice so far.

A Set-theoretic Approach to Reasoning Services for the Description Logic 𝒟 ℒ D 4,×

2020 ◽  
Vol 176 (3-4) ◽  
pp. 349-384
Author(s):  
Domenico Cantone ◽  
Marianna Nicolosi-Asmundo ◽  
Daniele Francesco Santamaria
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Theoretic Approach ◽  
The Novel ◽  
Data Types ◽  
Left Hand ◽  
Rule Languages ◽  
Tableau System ◽  
High Scalability ◽  
Better Than

In this paper we consider the most common TBox and ABox reasoning services for the description logic 𝒟ℒ〈4LQSR,x〉(D) ( 𝒟 ℒ D 4,× , for short) and prove their decidability via a reduction to the satisfiability problem for the set-theoretic fragment 4LQSR. 𝒟 ℒ D 4,× is a very expressive description logic. It combines the high scalability and efficiency of rule languages such as the SemanticWeb Rule Language (SWRL) with the expressivity of description logics. In fact, among other features, it supports Boolean operations on concepts and roles, role constructs such as the product of concepts and role chains on the left-hand side of inclusion axioms, role properties such as transitivity, symmetry, reflexivity, and irreflexivity, and data types. We further provide a KE-tableau-based procedure that allows one to reason on the main TBox and ABox reasoning tasks for the description logic 𝒟 ℒ D 4,× . Our algorithm is based on a variant of the KE-tableau system for sets of universally quantified clauses, where the KE-elimination rule is generalized in such a way as to incorporate the γ-rule. The novel system, called KEγ-tableau, turns out to be an improvement of the system introduced in [1] and of standard first-order KE-tableaux [2]. Suitable benchmark test sets executed on C++ implementations of the three mentioned systems show that in several cases the performances of the KEγ-tableau-based reasoner are up to about 400% better than the ones of the other two systems.

scholarly journals Capability-oriented architectural analysis method based on fuzzy description logic

2016 ◽  
Vol 13 (1) ◽  
pp. 287-308 ◽  
Author(s):  
Zhang Tingting ◽  
Liu Xiaoming ◽  
Wang Zhixue ◽  
Dong Qingchao
Keyword(s):  
Business Strategy ◽  
Domain Knowledge ◽  
Description Logic ◽  
Description Logics ◽  
Model Verification ◽  
Architectural Analysis ◽  
Requirements Modeling ◽  
Strategy Model ◽  
Domain Specific Modeling ◽  
Fuzzy Description

A number of problems may arise from architectural requirements modeling, including alignment of it with business strategy, model integration and handling the uncertain and vague information. The paper introduces a method for modeling architectural requirements in a way of ontology-based and capability-oriented requirements elicitation. The requirements can be modeled within a three-layer framework. The Capability Meta-concept Framework is provided at the top level. The domain experts can capture the domain knowledge within the framework, forming the domain ontology at the second level. The domain concepts can be used for extending the UML to produce a domain-specific modeling language. A fuzzy UML is introduced to model the vague and uncertain features of the capability requirements. An algorithm is provided to transform the fuzzy UML models into the fuzzy Description Logics ontology for model verification. A case study is given to demonstrate the applicability of the method.

scholarly journals Unifying Class-Based Representation Formalisms

1999 ◽  
Vol 11 ◽  
pp. 199-240 ◽  
Author(s):  
D. Calvanese ◽  
M. Lenzerini ◽  
D. Nardi
Keyword(s):  
Knowledge Representation ◽  
Description Logic ◽  
Description Logics ◽  
Expressive Power ◽  
Finite Model ◽  
Functional Dependencies ◽  
Semantic Data ◽  
Representation Systems ◽  
Frame Systems ◽  
Essential Set

The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues underlying such representation formalisms and single out both their common characteristics and their distinguishing features. Such investigation leads us to propose a unifying framework in which we are able to capture the fundamental aspects of several representation languages used in different contexts. The proposed formalism is expressed in the style of description logics, which have been introduced in knowledge representation as a means to provide a semantically well-founded basis for the structural aspects of knowledge representation systems. The description logic considered in this paper is a subset of first order logic with nice computational characteristics. It is quite expressive and features a novel combination of constructs that has not been studied before. The distinguishing constructs are number restrictions, which generalize existence and functional dependencies, inverse roles, which allow one to refer to the inverse of a relationship, and possibly cyclic assertions, which are necessary for capturing real world domains. We are able to show that it is precisely such combination of constructs that makes our logic powerful enough to model the essential set of features for defining class structures that are common to frame systems, object-oriented database languages, and semantic data models. As a consequence of the established correspondences, several significant extensions of each of the above formalisms become available. The high expressiveness of the logic we propose and the need for capturing the reasoning in different contexts forces us to distinguish between unrestricted and finite model reasoning. A notable feature of our proposal is that reasoning in both cases is decidable. We argue that, by virtue of the high expressive power and of the associated reasoning capabilities on both unrestricted and finite models, our logic provides a common core for class-based representation formalisms.

Logics for the Semantic Web

2011 ◽  
pp. 24-43
Author(s):  
J. Bruijn
Keyword(s):  
Semantic Web ◽  
Logic Programming ◽  
Description Logic ◽  
Description Logics ◽  
Order Logic ◽  
First Order Logic ◽  
Horn Logic ◽  
First Order ◽  
Logical Language ◽  
Rule Languages

This chapter introduces a number of formal logical languages which form the backbone of the Semantic Web. They are used for the representation of both ontologies and rules. The basis for all languages presented in this chapter is the classical first-order logic. Description logics is a family of languages which represent subsets of first-order logic. Expressive description logic languages form the basis for popular ontology languages on the Semantic Web. Logic programming is based on a subset of first-order logic, namely Horn logic, but uses a slightly different semantics and can be extended with non-monotonic negation. Many Semantic Web reasoners are based on logic programming principles and rule languages for the Semantic Web based on logic programming are an ongoing discussion. Frame Logic allows object-oriented style (frame-based) modeling in a logical language. RuleML is an XML-based syntax consisting of different sublanguages for the exchange of specifications in different logical languages over the Web.

A description logic based approach to formalizing the information bearing capability of paths in ER schemata

2015 ◽  
Vol 8 (3) ◽  
pp. 279-291
Author(s):  
Kaibo Xu ◽  
Junkang Feng ◽  
Malcolm Crowe ◽  
Lin Liu
Keyword(s):  
Design Methodology ◽  
Description Logic ◽  
Description Logics ◽  
Data Representation ◽  
Point Of View ◽  
Content Type ◽  
Data Dependencies ◽  
Entity Relationship ◽  
Evaluation Of Data ◽  
Data Construct

Purpose – The purpose of this paper is to show how description logics (DLs) can be applied to formalizing the information bearing capability (IBC) of paths in entity-relationship (ER) schemata. Design/methodology/approach – The approach follows and extends the idea presented in Xu and Feng (2004), which applies DLs to classifying paths in an ER schema. To verify whether the information content of a data construct (e.g. a path) covers a semantic relation (which formulates a piece of information requirement), the principle of IBC under the source-bearer-receiver framework is presented. It is observed that the IBC principle can be formalized by constructing DL expressions and examining constructors (e.g. quantifiers). Findings – Description logic can be used as a tool to describe the meanings represented by paths in an ER schema and formalize their IBC. The criteria for identifying data construct distinguishability are also discovered by examining quantifiers in DL expressions of paths of an ER schema. Originality/value – This paper focuses on classifying paths in data schemas and verifying their formalized IBC by using DLs and the IBC principle. It is a new point of view for evaluation of data representation, which looks at the information borne by data but not data dependencies.

The Applications of Description Logics in Natural Language Processing

2011 ◽  
Vol 181-182 ◽  
pp. 236-241
Author(s):  
Xian Yi Cheng ◽  
Chen Cheng ◽  
Qian Zhu
Keyword(s):  
Natural Language Processing ◽  
Natural Language ◽  
Language Processing ◽  
Domain Knowledge ◽  
Description Logic ◽  
Description Logics ◽  
Semantic Interpretation ◽  
Natural Language Semantic ◽  
Ontology Language ◽  
Basic Ideas

As a sort of formalizing tool of knowledge representation, Description Logics have been successfully applied in Information System, Software Engineering and Natural Language processing and so on. Description Logics also play a key role in text representation, Natural Language semantic interpretation and language ontology description. Description Logics have been logical basis of OWL which is an ontology language that is recommended by W3C. This paper discusses the description logic basic ideas under vocabulary semantic, context meaning, domain knowledge and background knowledge.

scholarly journals Conjunctive Query Answering for the Description Logic SHIQ

2008 ◽  
Vol 31 ◽  
pp. 157-204 ◽  
Author(s):  
B. Glimm ◽  
C. Lutz ◽  
I. Horrocks ◽  
U. Sattler
Keyword(s):  
Description Logic ◽  
Query Language ◽  
Description Logics ◽  
Knowledge Bases ◽  
Deterministic Algorithm ◽  
Query Answering ◽  
Conjunctive Query ◽  
Conjunctive Queries ◽  
Complexity Bounds ◽  
Double Exponential

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 knowledge bases formulated in the prominent DL SHIQ and allow transitive roles in both the query and the knowledge base. We show decidability of query answering in this setting and establish two tight complexity bounds: regarding combined complexity, we prove that there is a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query, which is optimal. Regarding data complexity, we prove containment in co-NP.

scholarly journals Constructing and Extending Description Logic Ontologies using Methods of Formal Concept Analysis

2020 ◽  
Vol 34 (3) ◽  
pp. 399-403 ◽  
Author(s):  
Francesco Kriegel
Keyword(s):  
Formal Concept Analysis ◽  
Description Logic ◽  
Description Logics ◽  
Concept Analysis ◽  
Rank Function ◽  
Formal Concept ◽  
Graded Lattice

Abstract My thesis describes how methods from Formal Concept Analysis can be used for constructing and extending description logic ontologies. In particular, it is shown how concept inclusions can be axiomatized from data in the description logics $$\mathcal {E}\mathcal {L}$$ E L , $$\mathcal {M}$$ M , $$\textsf {Horn}$$ Horn -$$\mathcal {M}$$ M , and $$\textsf{Prob}\text{-}\mathcal {E}\mathcal {L}$$ Prob - E L . All proposed methods are not only sound but also complete, i.e., the result not only consists of valid concept inclusions but also entails each valid concept inclusion. Moreover, a lattice-theoretic view on the description logic $$\mathcal {E}\mathcal {L}$$ E L is provided. For instance, it is shown how upper and lower neighbors of $$\mathcal {E}\mathcal {L}$$ E L concept descriptions can be computed and further it is proven that the set of $$\mathcal {E}\mathcal {L}$$ E L concept descriptions forms a graded lattice with a non-elementary rank function.

On the Decidability of Expressive Description Logics with Transitive Closure and Regular Role Expressions

2020 ◽  
Author(s):  
Jean Christoph Jung ◽  
Carsten Lutz ◽  
Thomas Zeume
Keyword(s):  
Modal Logic ◽  
Description Logic ◽  
Transitive Closure ◽  
Description Logics ◽  
Regular Expressions ◽  
Linear Orders ◽  
Functional Roles

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 role expressions of the form r*. SHOIF^1 encompasses the extension of SHOIF with transitive closure of roles (when functional roles have no subroles) and the modal logic of linear orders and successor, with converse. Consequently, these logics are also decidable and NExpTime-complete.

Using the Semantic Web Rule Language in the Development of Ontology-Driven Applications

2010 ◽  
pp. 525-539 ◽  
Author(s):  
Martin O’Connor ◽  
Mark Musen ◽  
Amar Das
Keyword(s):  
Semantic Web ◽  
Description Logic ◽  
Deductive Reasoning ◽  
Description Logics ◽  
Open World ◽  
Closed World ◽  
Amount Of Knowledge ◽  
Open World Assumption ◽  
Formal Characteristic ◽  
Semantic Web Rule Language

The Semantic Web Rule Language (SWRL) is an expressive OWL-based rule language. SWRL allows users to write Horn-like rules that can be expressed in terms of OWL concepts to provide more powerful deductive reasoning capabilities than OWL alone. Semantically, SWRL is built on the same description logic foundation as OWL and provides similar strong formal guarantees when performing inference. Due to its description logics foundation, rule-based applications developed using SWRL have a number of relatively novel characteristics. For example, SWRL shares OWL’s open world assumption so certain types of rules that assume a closed world may be difficult or impossible to write in SWRL. In addition, all inference in SWRL is monotonic so deductions cannot be updated or retracted. These formal characteristic have a strong influence on the development and use of SWRL rules in ontology-driven applications. In this chapter, we describe the primary features of SWRL and outline how, despite some limitations, SWRL can be used to dramatically increase amount of knowledge that be represented in OWL ontologies.

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