scholarly journals Beth Definability in Expressive Description Logics

2013 ◽  
Vol 48 ◽  
pp. 347-414 ◽  
Author(s):  
B. Ten Cate ◽  
E. Franconi ◽  
I. Seylan
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Complete Classification ◽  
Property A ◽  
Explicit Definition ◽  
Finite Structures ◽  
Double Exponential ◽  
Beth Definability ◽  
Definition Of

The Beth definability property, a well-known property from classical logic, is investigated in the context of description logics: if a general L-TBox implicitly defines an L-concept in terms of a given signature, where L is a description logic, then does there always exist over this signature an explicit definition in L for the concept? This property has been studied before and used to optimize reasoning in description logics. In this paper a complete classification of Beth definability is provided for extensions of the basic description logic ALC with transitive roles, inverse roles, role hierarchies, and/or functionality restrictions, both on arbitrary and on finite structures. Moreover, we present a tableau-based algorithm which computes explicit definitions of at most double exponential size. This algorithm is optimal because it is also shown that the smallest explicit definition of an implicitly defined concept may be double exponentially long in the size of the input TBox. Finally, if explicit definitions are allowed to be expressed in first-order logic, then we show how to compute them in single exponential time.

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 Consequence-Based Reasoning for Description Logics with Disjunctions and Number Restrictions

2018 ◽  
Vol 63 ◽  
pp. 625-690 ◽  
Author(s):  
Andrew Bate ◽  
Boris Motik ◽  
Bernardo Cuenca Grau ◽  
David Tena Cucala ◽  
František Simančík ◽  
...  
Keyword(s):  
Description Logic ◽  
Practical Reasoning ◽  
Description Logics ◽  
Practical Implementation ◽  
First Order ◽  
Implementation Techniques ◽  
Important Addition ◽  
Logic Reasoning ◽  
Extensive Performance

Classification of description logic (DL) ontologies is a key computational problem in modern data management applications, so considerable effort has been devoted to the development and optimisation of practical reasoning calculi. Consequence-based calculi combine ideas from hypertableau and resolution in a way that has proved very effective in practice. However, existing consequence-based calculi can handle either Horn DLs (which do not support disjunction) or DLs without number restrictions. In this paper, we overcome this important limitation and present the first consequence-based calculus for deciding concept subsumption in the DL ALCHIQ+. Our calculus runs in exponential time assuming unary coding of numbers, and on ELH ontologies it runs in polynomial time. The extension to disjunctions and number restrictions is technically involved: we capture the relevant consequences using first-order clauses, and our inference rules adapt paramodulation techniques from first-order theorem proving. By using a well-known preprocessing step, the calculus can also decide concept subsumptions in SRIQ---a rich DL that covers all features of OWL 2 DL apart from nominals and datatypes. We have implemented our calculus in a new reasoner called Sequoia. We present the architecture of our reasoner and discuss several novel and important implementation techniques such as clause indexing and redundancy elimination. Finally, we present the results of an extensive performance evaluation, which revealed Sequoia to be competitive with existing reasoners. Thus, the calculus and the techniques we present in this paper provide an important addition to the repertoire of practical implementation techniques for description logic reasoning.

scholarly journals High-Order Variational Time Integrators for Particle Dynamics

2018 ◽  
Vol 9 (2) ◽  
pp. 34-49 ◽  
Author(s):  
E. Miglio ◽  
N. Parolini ◽  
M. Penati ◽  
R. Porcù
Keyword(s):  
Particle Dynamics ◽  
Complete Classification ◽  
High Order ◽  
Variational Integrators ◽  
Order Method ◽  
High Order Method ◽  
Time Integrators ◽  
Material Points ◽  
Definition Of

Abstract The general family of Galerkin variational integrators are analyzed and a complete classification of such methods is proposed. This classification is based upon the type of basis function chosen to approximate the trajectories of material points and the numerical quadrature formula used in time. This approach leads to the definition of arbitrarily high order method in time. The proposed methodology is applied to the simulation of brownout phenomena occurring in helicopter take-off and landing.

scholarly journals Acquiring Ontology Axioms through Mappings to Data Sources

2019 ◽  
Vol 11 (12) ◽  
pp. 260
Author(s):  
Floriana Di Pinto ◽  
Giuseppe De Giacomo ◽  
Domenico Lembo ◽  
Maurizio Lenzerini ◽  
Riccardo Rosati
Keyword(s):  
Knowledge Base ◽  
Description Logic ◽  
Description Logics ◽  
Data Access ◽  
Data Sources ◽  
New Concepts ◽  
Source Data ◽  
Meta Modeling ◽  
Definition Of ◽  
Do So

Although current languages used in ontology-based data access (OBDA) systems allow for mapping source data to instances of concepts and relations in the ontology, several application domains need more flexible tools for inferring knowledge from data, which are able to dynamically acquire axioms about new concepts and relations directly from the data. In this paper we introduce the notion of mapping-based knowledge base (MKB) to formalize the situation where both the extensional and the intensional level of the ontology are determined by suitable mappings to a set of data sources. This allows for making the intensional level of the ontology as dynamic as the extensional level traditionally is. To do so, we resort to the meta-modeling capabilities of higher-order description logics, in particular the description logic Hi ( DL-Lite R ) , which allows seeing concepts and relations as individuals, and vice versa. The challenge in this setting is to design efficient algorithms for answering queries posed to MKBs. Besides the definition of MKBs, our main contribution is to prove that answering instance queries posed to MKBs expressed in Hi ( DL-Lite R ) can be done efficiently.

Comparing Weak Admissibility Semantics to their Dung-style Counterparts -- Reduct, Modularization, and Strong Equivalence in Abstract Argumentation

2020 ◽  
Author(s):  
Ringo Baumann ◽  
Gerhard Brewka ◽  
Markus Ulbricht
Keyword(s):  
Complete Classification ◽  
Recursive Definition ◽  
Abstract Argumentation ◽  
Abstract Principle ◽  
Definition Of

Semantics based on weak admissibility were recently introduced to overcome a problem with self-defeating arguments that has not been solved for more than 25 years. The recursive definition of weak admissibility mainly relies on the notion of a reduct regarding a set E which only contains arguments which are neither in E, nor attacked by E. At first glance the reduct seems to be tailored for the weaker versions of Dung-style semantics only. In this paper we show that standard Dung semantics can be naturally reformulated using the reduct revealing that this concept is already implicit. We further identify a new abstract principle for semantics, so-called modularization describing how to obtain further extensions given an initial one. Its importance for the study of abstract argumentation semantics is shown by its ability to alternatively characterize classical and non-classical semantics. Moreover, we tackle the notion of strong equivalence via characterizing kernels and give a complete classification of the weak versions regarding well-known properties and postulates known from the literature.

scholarly journals Jumping pairs of Steiner bundles

2015 ◽  
Vol 27 (6) ◽  
Author(s):  
Enrique Arrondo ◽  
Simone Marchesi
Keyword(s):  
Complete Classification ◽  
Maximal Dimension ◽  
Definition Of

AbstractIn this work we introduce the definition of Schwarzenberger bundle on a Grassmannian. Recalling the notion of Steiner bundle, we generalize the concept of jumping pair for a Steiner bundle on a Grassmannian. After studying the jumping locus variety and bounding its dimension, we give a complete classification of Steiner bundles with jumping locus of maximal dimension, which all are Schwarzenberger bundles.

Development and Evaluation of Fuzzy Criteria for the Diagnosis of Rheumatoid Arthritis

1996 ◽  
Vol 35 (04/05) ◽  
pp. 334-342 ◽  
Author(s):  
K.-P. Adlassnig ◽  
G. Kolarz ◽  
H. Leitich
Keyword(s):  
Rheumatoid Arthritis ◽  
Reference Model ◽  
American Rheumatism Association ◽  
Uniform Definition ◽  
Sensitivity Rate ◽  
Fuzzy Techniques ◽  
Definition Of ◽  
Different Levels ◽  
Specificity Rate

Abstract:In 1987, the American Rheumatism Association issued a set of criteria for the classification of rheumatoid arthritis (RA) to provide a uniform definition of RA patients. Fuzzy set theory and fuzzy logic were used to transform this set of criteria into a diagnostic tool that offers diagnoses at different levels of confidence: a definite level, which was consistent with the original criteria definition, as well as several possible and superdefinite levels. Two fuzzy models and a reference model which provided results at a definite level only were applied to 292 clinical cases from a hospital for rheumatic diseases. At the definite level, all models yielded a sensitivity rate of 72.6% and a specificity rate of 87.0%. Sensitivity and specificity rates at the possible levels ranged from 73.3% to 85.6% and from 83.6% to 87.0%. At the superdefinite levels, sensitivity rates ranged from 39.0% to 63.7% and specificity rates from 90.4% to 95.2%. Fuzzy techniques were helpful to add flexibility to preexisting diagnostic criteria in order to obtain diagnoses at the desired level of confidence.

ABOUT THE PROBLEM OF CLASSIFICATION OF THE CONCEPTS OF INFORMATICS STUDIED AT SECONDARY SCHOOL

2018 ◽  
pp. 4-7
Author(s):  
S. I. Zenko
Keyword(s):  
Secondary School ◽  
Foreign Language ◽  
Computer Science ◽  
Parts Of Speech ◽  
The Third ◽  
The Cross ◽  
Definition Of

The article raises the problem of classification of the concepts of computer science and informatics studied at secondary school. The efficiency of creation of techniques of training of pupils in these concepts depends on its solution. The author proposes to consider classifications of the concepts of school informatics from four positions: on the cross-subject basis, the content lines of the educational subject "Informatics", the logical and structural interrelations and interactions of the studied concepts, the etymology of foreign-language and translated words in the definition of the concepts of informatics. As a result of the first classification general and special concepts are allocated; the second classification — inter-content and intra-content concepts; the third classification — stable (steady), expanding, key and auxiliary concepts; the fourth classification — concepts-nouns, conceptsverbs, concepts-adjectives and concepts — combinations of parts of speech.

Determining the discount rate when evaluating trade organizations: Some features

2020 ◽  
Vol 13 (1) ◽  
pp. 71-84
Author(s):  
E.A. Grigor'eva ◽  
A.S. Buzhikeeva
Keyword(s):  
Discount Rate ◽  
Economic Activity ◽  
Systems Approach ◽  
Market Value ◽  
Additional Risk ◽  
Evaluation Procedures ◽  
Analytical Research ◽  
Definition Of ◽  
Traditional Approaches

Subject. This article deals with the issues of determining the market value of the trading business, taking into account a number of characteristics. Objectives. The article aims to develop certain provisions of the methodology and practice of evaluating the business of trading organizations, namely, taking into account the additional risk of inventory feasibility when calculating the discount rate. Methods. For the study, we used a systems approach, and the cognition, and economic and analytical research methods. Results. The article presents a three-tiered classification of stocks and a definition of risk based on the criteria for dividing stocks by purpose, degree of implementation, and shelf life in accordance with the scale. Based on the classification, the article offers certain recommendations for determining the discount rate when evaluating trading organizations, aimed at taking into account additional risk. Conclusions. Various evaluation procedures within the framework of traditional approaches and methods in relation to trading organizations do not take into account risk specific to this type of economic activity. The proposed methodology for calculating the discount rate for trade organizations takes into account the features of their functioning.

State Failure and the Political Violence Phenomenon: A Comparative Analysis of Iraq and Syria Cases

2016 ◽  
Vol 4 (2) ◽  
pp. 170 ◽  
Author(s):  
K. Eylem Özkaya Lassalle
Keyword(s):  
Cold War ◽  
Political Violence ◽  
State Failure ◽  
The Political ◽  
Collective Violence ◽  
Short Run ◽  
Definition Of ◽  
The Cold War

The concept of failed state came to the fore with the end of the Cold War, the collapse of the USSR and the disintegration of Yugoslavia. Political violence is central in these discussions on the definition of the concept or the determination of its dimensions (indicators). Specifically, the level of political violence, the type of political violence and intensity of political violence has been broached in the literature. An effective classification of political violence can lead us to a better understanding of state failure phenomenon. By using Tilly’s classification of collective violence which is based on extent of coordination among violent actors and salience of short-run damage, the role played by political violence in state failure can be understood clearly. In order to do this, two recent cases, Iraq and Syria will be examined.

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