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

2013 ◽  
Vol 47 ◽  
pp. 741-808 ◽  
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.

Text Semantic Mining Model Based on the Algebra of Human Concept Learning

2012 ◽  
pp. 221-236 ◽  
Author(s):  
Jun Zhang ◽  
Xiangfeng Luo ◽  
Xiang He ◽  
Chuanliang Cai
Keyword(s):  
Knowledge Representation ◽  
Concept Learning ◽  
Large Scale ◽  
Construction Process ◽  
Semantic Mining ◽  
Lower Complexity ◽  
Mining Model ◽  
The Given ◽  
The Web ◽  
Better Than

Dealing with the large-scale text knowledge on the Web has become increasingly important with the development of the Web, yet it confronts with several challenges, one of which is to find out as much semantics as possible to represent text knowledge. As the text semantic mining process is also the knowledge representation process of text, this paper proposes a text knowledge representation model called text semantic mining model (TSMM) based on the algebra of human concept learning, which both carries rich semantics and is constructed automatically with a lower complexity. Herein, the algebra of human concept learning is introduced, which enables TSMM containing rich semantics. Then the formalization and the construction process of TSMM are discussed. Moreover, three types of reasoning rules based on TSMM are proposed. Lastly, experiments and the comparison with current text representation models show that the given model performs better than others.

scholarly journals DaRLing: A Datalog rewriter for OWL 2 RL ontological reasoning under SPARQL queries

2020 ◽  
Vol 20 (6) ◽  
pp. 958-973
Author(s):  
ALESSIO FIORENTINO ◽  
JESSICA ZANGARI ◽  
MARCO MANNA
Keyword(s):  
Knowledge Representation ◽  
Experimental Evaluation ◽  
Query Answering ◽  
Web Ontology Language ◽  
Web Resources ◽  
Rich Variety ◽  
Ontology Language ◽  
Ontological Reasoning ◽  
Powerful Knowledge ◽  
Representation Formalism

AbstractThe W3C Web Ontology Language (OWL) is a powerful knowledge representation formalism at the basis of many semantic-centric applications. Since its unrestricted usage makes reasoning undecidable already in case of very simple tasks, expressive yet decidable fragments have been identified. Among them, we focus on OWL 2 RL, which offers a rich variety of semantic constructors, apart from supporting all RDFS datatypes. Although popular Web resources - such as DBpedia - fall in OWL 2 RL, only a few systems have been designed and implemented for this fragment. None of them, however, fully satisfy all the following desiderata: (i) being freely available and regularly maintained; (ii) supporting query answering and SPARQL queries; (iii) properly applying the sameAs property without adopting the unique name assumption; (iv) dealing with concrete datatypes. To fill the gap, we present DaRLing, a freely available Datalog rewriter for OWL 2 RL ontological reasoning under SPARQL queries. In particular, we describe its architecture, the rewriting strategies it implements, and the result of an experimental evaluation that demonstrates its practical applicability.

scholarly journals Towards Universal Languages for Tractable Ontology Mediated Query Answering

2020 ◽  
Vol 34 (03) ◽  
pp. 3049-3056
Author(s):  
Heng Zhang ◽  
Yan Zhang ◽  
Jia-Huai You ◽  
Zhiyong Feng ◽  
Guifei Jiang
Keyword(s):  
Query Languages ◽  
Query Answering ◽  
Data Complexity ◽  
Conjunctive Queries ◽  
Negative Side ◽  
First Order ◽  
Positive Side ◽  
Universal Language ◽  
Ontology Language ◽  
The Family

An ontology language for ontology mediated query answering (OMQA-language) is universal for a family of OMQA-languages if it is the most expressive one among this family. In this paper, we focus on three families of tractable OMQA-languages, including first-order rewritable languages and languages whose data complexity of the query answering is in AC0 or PTIME. On the negative side, we prove that there is, in general, no universal language for each of these families of languages. On the positive side, we propose a novel property, the locality, to approximate the first-order rewritability, and show that there exists a language of disjunctive embedded dependencies that is universal for the family of OMQA-languages with locality. All of these results apply to OMQA with query languages such as conjunctive queries, unions of conjunctive queries and acyclic conjunctive queries.

Text Semantic Mining Model Based on the Algebra of Human Concept Learning

2011 ◽  
Vol 5 (2) ◽  
pp. 80-96
Author(s):  
Jun Zhang ◽  
Xiangfeng Luo ◽  
Xiang He ◽  
Chuanliang Cai
Keyword(s):  
Knowledge Representation ◽  
Concept Learning ◽  
Large Scale ◽  
Construction Process ◽  
Semantic Mining ◽  
Lower Complexity ◽  
Mining Model ◽  
The Given ◽  
The Web ◽  
Better Than

Dealing with the large-scale text knowledge on the Web has become increasingly important with the development of the Web, yet it confronts with several challenges, one of which is to find out as much semantics as possible to represent text knowledge. As the text semantic mining process is also the knowledge representation process of text, this paper proposes a text knowledge representation model called text semantic mining model (TSMM) based on the algebra of human concept learning, which both carries rich semantics and is constructed automatically with a lower complexity. Herein, the algebra of human concept learning is introduced, which enables TSMM containing rich semantics. Then the formalization and the construction process of TSMM are discussed. Moreover, three types of reasoning rules based on TSMM are proposed. Lastly, experiments and the comparison with current text representation models show that the given model performs better than others.

scholarly journals Answering Conjunctive Queries with Inequalities in DL-Liteℛ

2020 ◽  
Vol 34 (03) ◽  
pp. 2782-2789
Author(s):  
Gianluca Cima ◽  
Maurizio Lenzerini ◽  
Antonella Poggi
Keyword(s):  
Description Logic ◽  
Query Language ◽  
Query Answering ◽  
Data Complexity ◽  
Conjunctive Queries ◽  
Complexity Bounds ◽  
Ontology Language

In the context of the Description Logic DL-Liteℛ≠, i.e., DL-Liteℛ without UNA and with inequality axioms, we address the problem of adding to unions of conjunctive queries (UCQs) one of the simplest forms of negation, namely, inequality. It is well known that answering conjunctive queries with unrestricted inequalities over DL-Liteℛ ontologies is in general undecidable. Therefore, we explore two strategies for recovering decidability, and, hopefully, tractability. Firstly, we weaken the ontology language, and consider the variant of DL-Liteℛ≠ corresponding to rdfs enriched with both inequality and disjointness axioms. Secondly, we weaken the query language, by preventing inequalities to be applied to existentially quantified variables, thus obtaining the class of queries named UCQ≠,bs. We prove that in the two cases, query answering is decidable, and we provide tight complexity bounds for the problem, both for data and combined complexity. Notably, the results show that answering UCQ≠,bs over DL-Liteℛ≠ ontologies is still in AC0 in data complexity.

scholarly journals Answering Counting Queries over DL-Lite Ontologies

2020 ◽  
Author(s):  
Meghyn Bienvenu ◽  
Quentin Manière ◽  
Michaël Thomazo
Keyword(s):  
Knowledge Representation ◽  
Data Access ◽  
Query Answering ◽  
High Complexity ◽  
Conjunctive Queries ◽  
Complexity Bounds

Ontology-mediated query answering (OMQA) is a promising approach to data access and integration that has been actively studied in the knowledge representation and database communities for more than a decade. The vast majority of work on OMQA focuses on conjunctive queries, whereas more expressive queries that feature counting or other forms of aggregation remain largely unexplored. In this paper, we introduce a general form of counting query, relate it to previous proposals, and study the complexity of answering such queries in the presence of DL-Lite ontologies. As it follows from existing work that query answering is intractable and often of high complexity, we consider some practically relevant restrictions, for which we establish improved complexity bounds.

Approximating the stationary distribution of an infinite stochastic matrix

1991 ◽  
Vol 28 (1) ◽  
pp. 96-103 ◽  
Author(s):  
Daniel P. Heyman
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Stationary Distribution ◽  
Numerical Approximation ◽  
Stochastic Matrix ◽  
Sufficient Conditions ◽  
Finite System ◽  
Balance Equations ◽  
The Given ◽  
Steady State Balance

We are given a Markov chain with states 0, 1, 2, ···. We want to get a numerical approximation of the steady-state balance equations. To do this, we truncate the chain, keeping the first n states, make the resulting matrix stochastic in some convenient way, and solve the finite system. The purpose of this paper is to provide some sufficient conditions that imply that as n tends to infinity, the stationary distributions of the truncated chains converge to the stationary distribution of the given chain. Our approach is completely probabilistic, and our conditions are given in probabilistic terms. We illustrate how to verify these conditions with five examples.

scholarly journals Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xinru Liu ◽  
Yuanpeng Zhu ◽  
Shengjun Liu
Keyword(s):  
Sufficient Conditions ◽  
Rational Interpolation ◽  
Rectangular Domain ◽  
Interpolation Spline ◽  
Spline Surface ◽  
Surface Data ◽  
Shape Preserving Interpolation ◽  
The Given ◽  
Surface Construction ◽  
Special Case

A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively.

Creative Design Methodology and the SIT Method

1997 ◽  
Author(s):  
Roni Horowitz ◽  
Oded Maimon
Keyword(s):  
Design Methodology ◽  
Search Strategy ◽  
Sufficient Conditions ◽  
Strategy Selection ◽  
Step Procedure ◽  
Creative Solutions ◽  
General Search ◽  
Problem Reformulation ◽  
Creative Problem ◽  
The Given

Abstract The paper presents SIT (Structured Inventive Thinking) — a structured method for enhancing creative problem solving in engineering design. The method is a three step procedure: problem reformulation, general search strategy selection, and an application of idea provoking techniques. The most innovative part of the method is the problem reformulation stage. The given problem is modified through the application of objectively defined and empirically tested set of sufficient conditions for creative solutions. The paper describes the sufficient conditions and the empirical study that demonstrates their appropriateness. Then the whole SIT mechanism is presented with illustrative examples.

On two pursuit differential game problems with state and geometric constraints in a Hilbert space

2021 ◽  
Vol 65 (3) ◽  
pp. 5-16
Author(s):  
Abbas Ja’afaru Badakaya ◽  
Keyword(s):  
Differential Game ◽  
Convex Set ◽  
Sufficient Conditions ◽  
Nonempty Closed Convex Subset ◽  
Geometric Constraints ◽  
First Order ◽  
Control Functions ◽  
Closed Convex Set ◽  
The Given ◽  
First Order Differential Equations

This paper concerns with the study of two pursuit differential game problems of many pursuers and many evaders on a nonempty closed convex subset of R^n. Throughout the period of the games, players must stay within the given closed convex set. Players’ laws of motion are defined by certain first order differential equations. Control functions of the pursuers and evaders are subject to geometric constraints. Pursuit is said to be completed if the geometric position of each of the evader coincides with that of a pursuer. We proved two theorems each of which is solution to a problem. Sufficient conditions for the completion of pursuit are provided in each of the theorems. Moreover, we constructed strategies of the pursuers that ensure completion of pursuit.

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