scholarly journals On Concept Forgetting in Description Logics with Qualified Number Restrictions

2018 ◽  
Author(s):  
Yizheng Zhao ◽  
Renate Schmidt
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Practical Method ◽  
Test Cases ◽  
Biomedical Ontologies ◽  
Large Corpus

This paper presents a practical method for computing solutions of concept forgetting in the description logic ALCOQ(neg,and,or), basic ALC extended with nominals, qualified number restrictions, role negation, role conjunction and role disjunction. The method is based on a non-trivial generalisation of Ackermann's Lemma, and attempts to compute either semantic solutions of concept forgetting or uniform interpolants in ALCOQ(neg,and,or). It is so far the only approach to concept forgetting in description logics with number restrictions plus nominals, as well as in description logics with ABoxes. Results of an evaluation with a prototypical implementation have shown that the method was successful in more than 90% of the test cases from a large corpus of biomedical ontologies. In only 13.2% of these cases the solutions were semantic solutions.

scholarly journals A Practical Approach to Forgetting in Description Logics with Nominals

2020 ◽  
Vol 34 (03) ◽  
pp. 3073-3079
Author(s):  
Yizheng Zhao ◽  
Renate Schmidt ◽  
Yuejie Wang ◽  
Xuanming Zhang ◽  
Hao Feng
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Practical Method ◽  
Practical Approach ◽  
Ontology Engineering ◽  
Success Rates ◽  
Prototype Implementation ◽  
Speed Up

This paper investigates the problem of forgetting in description logics with nominals. In particular, we develop a practical method for forgetting concept and role names from ontologies specified in the description logic ALCO, extending the basic ALC with nominals. The method always terminates, and is sound in the sense that the forgetting solution computed by the method has the same logical consequences with the original ontology. The method is so far the only approach to deductive forgetting in description logics with nominals. An evaluation of a prototype implementation shows that the method achieves a significant speed-up and notably better success rates than the Lethe tool which performs deductive forgetting for ALC-ontologies. Compared to Fame, a semantic forgetting tool for ALCOIH-ontologies, better success rates are attained. From the perspective of ontology engineering this is very useful, as it provides ontology curators with a powerful tool to produce views of ontologies.

scholarly journals Hybrid Unification in the Description Logic EL

10.29007/h59c ◽  
2018 ◽  
Author(s):  
Franz Baader ◽  
Oliver Fernandez Gil ◽  
Barbara Morawska
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
General Concept ◽  
Biomedical Ontologies ◽  
Declarative Semantics ◽  
Np Complete ◽  
Unification Algorithms

Unification in Description Logics (DLs) has been proposed as an inferenceservice that can, for example, be used to detect redundancies in ontologies.For the DL EL, which is used to define several largebiomedical ontologies, unification is NP-complete. However, the unification algorithms for EL developeduntil recently could not deal with ontologies containing general concept inclusions (GCIs).In a series of recent papers we have made some progress towards addressing this problem, but the ontologies thedeveloped unification algorithms can deal with need to satisfy a certain cycle restriction.In the present paper, we follow a different approach. Instead of restricting the input ontologies,we generalize the notion of unifiers to so-called hybrid unifiers. Whereas classical unifiers can be viewed as acyclic TBoxes,hybrid unifiers are cyclic TBoxes, which are interpreted together with the ontology of the input using a hybrid semantics thatcombines fixpoint and declarative semantics. We show that hybrid unification in EL is NP-complete

scholarly journals Role Forgetting for ALCOQH(universal role)-Ontologies Using an Ackermann-Based Approach

2017 ◽  
Author(s):  
Yizheng Zhao ◽  
Renate A. Schmidt
Keyword(s):  
Real World ◽  
Description Logic ◽  
Description Logics ◽  
Practical Method ◽  
Semantic Role ◽  
Success Rates ◽  
Reasoning Problem ◽  
Performance Results

Forgetting refers to a non-standard reasoning problem concerned with eliminating concept and role symbols from description logic-based ontologies while preserving all logical consequences up to the remaining symbols. Whereas previous research has primarily focused on forgetting concept symbols, in this paper, we turn our attention to role symbol forgetting. In particular, we present a practical method for semantic role forgetting for ontologies expressible in the description logic ALCOQH(universal role), i.e., the basic description logic ALC extended with nominals, qualified number restrictions, role inclusions and the universal role. Being based on an Ackermann approach, the method is the only approach so far for forgetting role symbols in description logics with qualified number restrictions. The method is goal-oriented and incremental. It always terminates and is sound in the sense that the forgetting solution is equivalent to the original ontology up to the forgotten symbols possibly with new concept definer symbols. Despite our method not being complete, performance results of an evaluation with a prototypical implementation have shown very good success rates on real-world ontologies.

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.

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