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.

Ontologies and Medical Terminologies

2011 ◽  
pp. 1463-1469
Author(s):  
James Geller
Keyword(s):  
Knowledge Representation ◽  
Computer Science ◽  
World Wide ◽  
Semantic Networks ◽  
Systematic Account ◽  
Area Of Interest ◽  
Representation Systems ◽  
Classical Paper ◽  
Interchange Format ◽  
Frame Systems

The term “Ontology” was popularized in Computer Science by Thomas Gruber at the Stanford Knowledge Systems Lab (KSL). Gruber’s highly influential papers defined an ontology as “an explicit specification of a conceptualization.” (Gruber, 1992; Gruber 1993). Gruber cited a conceptualization as being “the objects and concepts, and other entities that are assumed to exist in some area of interest and the relationships that hold among them.” (Genesereth & Nilsson, 1987). The term “Ontology” has been used in computer science at least since (Neches, 1991), but is derived from philosophy where it defines a “systematic account of existence,” usually contrasted with “Epistemology.” Gruber’s work is firmly grounded in Knowledge Representation and Artificial Intelligence research going back to McCarthy and Hayes classical paper (McCarthy & Hayes, 1969). Gruber’s work also builds on frame systems (Minsky, 1975; Fikes and Kehler, 1985) which have their roots in Semantic Networks, pioneered by (Quillian, 1968) and popularized through the successful and widespread KL-ONE family (Brachman & Schmolze, 1985). One can argue that Gruber’s ontologies are structurally very close to previous work in frame-based knowledge representation systems. However, Gruber focused on the notion of knowledge sharing which was a popular topic at KSL around the same time, especially in the form of the Knowledge Interchange Format (KIF) (Genesereth, 1991). Ontologies have recently moved center stage in Computer Science as they are a major ingredient of the Semantic Web (Berners-Lee et al., 2001), the next generation of the World-Wide Web. Ontologies have also been used in Data Mining (see below) and in (database) schema integration.

scholarly journals On Free Description Logics with Definite Descriptions

2021 ◽  
Author(s):  
Alessandro Artale ◽  
Andrea Mazzullo ◽  
Ana Ozaki ◽  
Frank Wolter
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Expressive Power ◽  
Definite Descriptions ◽  
First Order ◽  
Domain Semantics ◽  
Automated Support ◽  
Suitable Notion ◽  
Dual Domain ◽  
Polynomial Time Reduction

Definite descriptions are phrases of the form ‘the x such that φ’, used to refer to single entities in a context. They are often more meaningful to users than individual names alone, in particular when modelling or querying data over ontologies. We investigate free description logics with both individual names and definite descriptions as terms of the language, while also accounting for their possible lack of denotation. We focus on the extensions of ALC and, respectively, EL with nominals, the universal role, and definite descriptions. We show that standard reasoning in these extensions is not harder than in the original languages, and we characterise the expressive power of concepts relative to first-order formulas using a suitable notion of bisimulation. Moreover, we lay the foundations for automated support for definite descriptions generation by studying the complexity of deciding the existence of definite descriptions for an individual under an ontology. Finally, we provide a polynomial-time reduction of reasoning in other free description logic languages based on dual-domain semantics to the case of partial interpretations.

A Modal Logic for Similarity Relations in Pawlak Knowledge Representation Systems

1991 ◽  
Vol 15 (1) ◽  
pp. 61-79
Author(s):  
Dimiter Vakarelov
Keyword(s):  
Modal Logic ◽  
Knowledge Representation ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property ◽  
First Order ◽  
Similarity Relations ◽  
Representation Systems ◽  
Knowledge Representation Systems

One of the main results of the paper is a characterization of certain kind similarity relations in Pawlak knowledge representation systems by means of first order sentences. As an application we obtain a complete finite axiomatization of the corresponding poly modal logic, called in the paper MLSim. It is proved that MLSim possesses finite model property and is decidable.

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 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 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 A Characterization Theorem for a Modal Description Logic

2017 ◽  
Author(s):  
Paul Wild ◽  
Lutz Schröder
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Characterization Theorem ◽  
Expressive Power ◽  
Order Logic ◽  
First Order Logic ◽  
Standard Description ◽  
First Order ◽  
Information State ◽  
Modal Description

Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combines the standard description logic ALC with an S5-modality that can be understood as an epistemic operator or as representing (undirected) change. This logic embeds into a corresponding modal first-order logic S5-FOL. We prove a modal characterization theorem for this embedding, in analogy to results by van Benthem and Rosen relating ALC to standard first-order logic: We show that S5-ALC with only local roles is, both over finite and over unrestricted models, precisely the bisimulation-invariant fragment of S5-FOL, thus giving an exact description of the expressive power of S5-ALC with only local roles.

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).

Efficient knowledge representation systems

1990 ◽  
Vol 5 (1) ◽  
pp. 35-50
Author(s):  
Dario Giuse
Keyword(s):  
Knowledge Representation ◽  
High Performance ◽  
Object Oriented Programming ◽  
Important Place ◽  
Representation Systems ◽  
Frame System ◽  
Computer Based ◽  
Frame Systems ◽  
Flexible Knowledge ◽  
Knowledge Representation Systems

AbstractFrame systems occupy an important place among formalisms for computer-based knowledge representation. A common concern about frame systems, however, is that they are not efficient enough. We argue that this is not necessarily true of all possible systems, and that the trade-off between generality and efficiency has not been fully explored. While many systems provide generality at the expense of performance, systems closer to the low end of the spectrum have not been investigated nearly as much. Those systems are well suited for applications that need flexible knowledge representation but cannot afford the high performance price.We describe in detail KR, a very efficient frame system that provides mechanisms for knowledge representation including user-defined inheritance and relations, object-oriented programming, and constraint maintenance. The system is simple and compact and does not include some of the more complex functionality, but it is highly optimized and offers excellent performance for a variety of applications.

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