scholarly journals Hypertableau Reasoning for Description Logics

2009 ◽  
Vol 36 ◽  
pp. 165-228 ◽  
Author(s):  
B. Motik ◽  
R. Shearer ◽  
I. Horrocks
Keyword(s):  
Semantic Web ◽  
Knowledge Representation ◽  
Description Logic ◽  
State Of The Art ◽  
Description Logics ◽  
Primary Sources ◽  
Performance Improvements ◽  
Introduction Rule ◽  
Significant Performance ◽  
Representation Formalism

We present a novel reasoning calculus for the description logic SHOIQ^+---a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableau-based reasoning calculi used in state-of-the-art reasoners. In order to reduce nondeterminism, we base our calculus on hypertableau and hyperresolution calculi, which we extend with a blocking condition to ensure termination. In order to reduce the size of the constructed models, we introduce anywhere pairwise blocking. We also present an improved nominal introduction rule that ensures termination in the presence of nominals, inverse roles, and number restrictions---a combination of DL constructs that has proven notoriously difficult to handle. Our implementation shows significant performance improvements over state-of-the-art reasoners on several well-known ontologies.

scholarly journals Semantic Matchmaking as Non-Monotonic Reasoning: A Description Logic Approach

2007 ◽  
Vol 29 ◽  
pp. 269-307 ◽  
Author(s):  
T. Di Noia ◽  
E. Di Sciascio ◽  
F. M. Donini
Keyword(s):  
Semantic Web ◽  
Knowledge Representation ◽  
Web Service ◽  
Description Logic ◽  
Supply And Demand ◽  
Description Logics ◽  
Semantic Web Services ◽  
Logical Framework ◽  
Electronic Marketplace ◽  
Logic Approach

Matchmaking arises when supply and demand meet in an electronic marketplace, or when agents search for a web service to perform some task, or even when recruiting agencies match curricula and job profiles. In such open environments, the objective of a matchmaking process is to discover best available offers to a given request. We address the problem of matchmaking from a knowledge representation perspective, with a formalization based on Description Logics. We devise Concept Abduction and Concept Contraction as non-monotonic inferences in Description Logics suitable for modeling matchmaking in a logical framework, and prove some related complexity results. We also present reasonable algorithms for semantic matchmaking based on the devised inferences, and prove that they obey to some commonsense properties. Finally, we report on the implementation of the proposed matchmaking framework, which has been used both as a mediator in e-marketplaces and for semantic web services discovery.

scholarly journals Configuration knowledge representations for Semantic Web applications

2003 ◽  
Vol 17 (1) ◽  
pp. 31-50 ◽  
Author(s):  
ALEXANDER FELFERNIG ◽  
GERHARD FRIEDRICH ◽  
DIETMAR JANNACH ◽  
MARKUS STUMPTNER ◽  
MARKUS ZANKER
Keyword(s):  
Problem Solving ◽  
Semantic Web ◽  
Knowledge Representation ◽  
Web Applications ◽  
Description Logic ◽  
Predicate Logic ◽  
Description Logics ◽  
Formal Semantics ◽  
Problem Definition ◽  
Configuration Problem

Today's economy exhibits a growing trend toward highly specialized solution providers cooperatively offering configurable products and services to their customers. This paradigm shift requires the extension of current standalone configuration technology with capabilities of knowledge sharing and distributed problem solving. In this context a standardized configuration knowledge representation language with formal semantics is needed in order to support knowledge interchange between different configuration environments. Languages such as Ontology Inference Layer (OIL) and DARPA Agent Markup Language (DAML+OIL) are based on such formal semantics (description logic) and are very popular for knowledge representation in the Semantic Web. In this paper we analyze the applicability of those languages with respect to configuration knowledge representation and discuss additional demands on expressivity. For joint configuration problem solving it is necessary to agree on a common problem definition. Therefore, we give a description logic based definition of a configuration problem and show its equivalence with existing consistency-based definitions, thus joining the two major streams in knowledge-based configuration (description logics and predicate logic/constraint based configuration).

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.

iHDT++: improving HDT for SPARQL triple pattern resolution

2020 ◽  
Vol 39 (2) ◽  
pp. 2249-2261
Author(s):  
Antonio Hernández-Illera ◽  
Miguel A. Martínez-Prieto ◽  
Javier D. Fernández ◽  
Antonio Fariña
Keyword(s):  
State Of The Art ◽  
Simple Design ◽  
Performance Improvements ◽  
Semantic Data ◽  
Object Based ◽  
Efficient Access ◽  
Memory Footprint ◽  
Significant Performance ◽  
Pattern Resolution

RDF self-indexes compress the RDF collection and provide efficient access to the data without a previous decompression (via the so-called SPARQL triple patterns). HDT is one of the reference solutions in this scenario, with several applications to lower the barrier of both publication and consumption of Big Semantic Data. However, the simple design of HDT takes a compromise position between compression effectiveness and retrieval speed. In particular, it supports scan and subject-based queries, but it requires additional indexes to resolve predicate and object-based SPARQL triple patterns. A recent variant, HDT++, improves HDT compression ratios, but it does not retain the original HDT retrieval capabilities. In this article, we extend HDT++ with additional indexes to support full SPARQL triple pattern resolution with a lower memory footprint than the original indexed HDT (called HDT-FoQ). Our evaluation shows that the resultant structure, iHDT++ , requires 70 - 85% of the original HDT-FoQ space (and up to 48 - 72% for an HDT Community variant). In addition, iHDT++ shows significant performance improvements (up to one level of magnitude) for most triple pattern queries, being competitive with state-of-the-art RDF self-indexes.

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.

scholarly journals Incremental Tabling in Support of Knowledge Representation and Reasoning

2014 ◽  
Vol 14 (4-5) ◽  
pp. 553-567 ◽  
Author(s):  
TERRANCE SWIFT
Keyword(s):  
Knowledge Representation ◽  
Knowledge Representation And Reasoning ◽  
Semantic Level ◽  
Performance Improvements ◽  
Significant Performance ◽  
Dependency Structures ◽  
Dynamic Updates ◽  
And Control ◽  
Tabled Resolution

AbstractResolution-based Knowledge Representation and Reasoning (KRR) systems, such as Flora-2, Silk or Ergo, can scale to tens or hundreds of millions of facts, while supporting reasoning that includes Hilog, inheritance, defeasibility theories, and equality theories. These systems handle the termination and complexity issues that arise from the use of these features by a heavy use of tabled resolution. In fact, such systems table by default all rules defined by users, unless they are simple facts.Performing dynamic updates within such systems is nearly impossible unless the tables themselves can be made to react to changes. Incremental tabling as first implemented in XSB (Saha 2006) partially addressed this problem, but the implementation was limited in scope and not always easy to use. In this paper, we introducetransparent incremental tablingwhich at the semantic level supports updates in the 3-valued well-founded semantics, while guaranteeing full consistency of all tabled queries. Transparent incremental tabling also has significant performance improvements over previous implementations, including lazy recomputation, and control over the dependency structures used to determine how tables are updated.

The Probabilistic Description Logic

2020 ◽  
pp. 1-24
Author(s):  
LEONARD BOTHA ◽  
THOMAS MEYER ◽  
RAFAEL PEÑALOZA
Keyword(s):  
Knowledge Representation ◽  
Description Logic ◽  
Description Logics ◽  
Light Weight ◽  
Classical Form ◽  
First Order ◽  
Probabilistic Description

Abstract Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. Due to their first-order semantics, these languages (in their classical form) are not suitable for representing and handling uncertainty. A probabilistic extension of a light-weight DL was recently proposed for dealing with certain knowledge occurring in uncertain contexts. In this paper, we continue that line of research by introducing the Bayesian extension of the propositionally closed DL . We present a tableau-based procedure for deciding consistency and adapt it to solve other probabilistic, contextual, and general inferences in this logic. We also show that all these problems remain ExpTime-complete, the same as reasoning in the underlying classical .

scholarly journals A Semantics and Complete Algorithm for Subsumption in the CLASSIC Description Logic

1994 ◽  
Vol 1 ◽  
pp. 277-308 ◽  
Author(s):  
A. Borgida ◽  
P. F. Patel-Schneider
Keyword(s):  
Standard Model ◽  
Knowledge Representation ◽  
Description Logic ◽  
Description Logics ◽  
Representation System ◽  
Practical Applications ◽  
Current Implementation ◽  
The Standard Model ◽  
Soundness And Completeness ◽  
Knowledge Representation System

This paper analyzes the correctness of the subsumption algorithm used in CLASSIC, a description logic-based knowledge representation system that is being used in practical applications. In order to deal efficiently with individuals in CLASSIC descriptions, the developers have had to use an algorithm that is incomplete with respect to the standard, model-theoretic semantics for description logics. We provide a variant semantics for descriptions with respect to which the current implementation is complete, and which can be independently motivated. The soundness and completeness of the polynomial-time subsumption algorithm is established using description graphs, which are an abstracted version of the implementation structures used in CLASSIC, and are of independent interest.

scholarly journals Loop formulas for description logic programs

2010 ◽  
Vol 10 (4-6) ◽  
pp. 531-545 ◽  
Author(s):  
YISONG WANG ◽  
JIA-HUAI YOU ◽  
LI YAN YUAN ◽  
YI-DONG SHEN
Keyword(s):  
Semantic Web ◽  
Description Logic ◽  
Description Logics ◽  
Answer Set Programming ◽  
Desirable Property ◽  
Logic Programs ◽  
Alternative Semantics ◽  
Answer Set Semantics ◽  
Answer Sets ◽  
Answer Set

AbstractDescription Logic Programs (dl-programs) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the notions of completion and loop formulas of logic programs to description logic programs and show that the answer sets of a dl-program can be precisely captured by the models of its completion and loop formulas. Furthermore, we propose a new, alternative semantics for dl-programs, called the canonical answer set semantics, which is defined by the models of completion that satisfy what are called canonical loop formulas. A desirable property of canonical answer sets is that they are free of circular justifications. Some properties of canonical answer sets are also explored.

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