2,111 research outputs found
Formalizing ontology alignment and its operations with category theory
zimmermann2006aInternational audienceAn ontology alignment is the expression of relations between different ontologies. In order to view alignments independently from the language expressing ontologies and from the techniques used for finding the alignments, we use a category-theoretical model in which ontologies are the objects. We introduce a categorical structure, called V-alignment, made of a pair of morphisms with a common domain having the ontologies as codomain. This structure serves to design an algebra that describes formally what are ontology merging, alignment compo- sition, union and intersection using categorical constructions. This enables combining alignments of various provenance. Although the desirable properties of this algebra make such abstract manipulation of V-alignments very simple, it is practically not well fitted for expressing complex alignments: expressing subsumption between entities of two different ontologies demands the definition of non-standard categories of ontologies. We consider two approaches to solve this problem. The first one extends the notion of V-alignments to a more complex structure called W-alignments: a formalization of alignments relying on "bridge axioms". The second one relies on an elaborate concrete category of ontologies that offers high expressive power. We show that these two extensions have different advantages that may be exploited in different contexts (v
The Information-Flow Approach to Ontology-Based Semantic Integration
In this article we argue for the lack of formal foundations for ontology-based semantic alignment. We analyse and formalise the basic notions of semantic matching and alignment and we situate them in the context of ontology-based alignment in open-ended and distributed environments, like the Web. We then use the mathematical notion of information flow in a distributed system to ground three hypotheses that enable semantic alignment. We draw our exemplar applications of this work from a variety of interoperability scenarios including ontology mapping, theory of semantic interoperability, progressive ontology alignment, and situated semantic alignment
Institutionalising Ontology-Based Semantic Integration
We address what is still a scarcity of general mathematical foundations for ontology-based semantic integration underlying current knowledge engineering methodologies in decentralised and distributed environments. After recalling the first-order ontology-based approach to semantic integration and a formalisation of ontological commitment, we propose a general theory that uses a syntax-and interpretation-independent formulation of language, ontology, and ontological commitment in terms of institutions. We claim that our formalisation generalises the intuitive notion of ontology-based semantic integration while retaining its basic insight, and we apply it for eliciting and hence comparing various increasingly complex notions of semantic integration and ontological commitment based on differing understandings of semantics
A proposal for ontology formalization based on category theory
This work proposes a formalization of domain ontologies based in category theory as a framework for the study and representation of conceptual models. Category theory is a branch of mathematics that studies the structure in systems of composable relations. Domain ontologies are conceptual models that enable the reuse of domain knowledge and the execution of inferential processes over said knowledge. In order to achieve such goals, concepts must be modeled intensionally. The established set-theoretic foundations of current conceptual models are incompatible with the intended intensionality of ontological models. Category theory, on the other hand, does not default to extensionality in the same way set theory does, and offers, therefore, a better-suited mathematical foundation. Additionally, category theory’s focus on relations matches the primary attention of construction and representation of ontologies, which is turned towards the relations between the domain concepts. The present work builds upon these motivations and formalizes ontologies as categories of concepts and conceptual relations. We subsequently analyze the categorical constructions present in ontologies, and the consequences of this formalization for categories of ontologies.O presente trabalho propõe uma formalização de ontologias de domínio baseada em teoria das categorias como um arcabouço para o estudo e representação de modelos conceituais. A teoria das categorias é uma área da matemática que estuda a estrutura presente em sistemas de relações componíveis. Ontologias de domínio são modelos conceituais que permitem o reuso de conhecimento de domínio e a execução de processos de inferência sobre tal conhecimento. Para atingir tais objetivos, os conceitos devem ser modelados de forma intensional. As fundamentações dos modelos conceituais baseadas em teoria dos conjuntos atualmente aceitas são incompatíveis com a pretendida intensionalidade de modelos ontológicos. A teoria das categorias, por outro lado, não está comprometida com extensionalidade da mesma forma que a teoria dos conjuntos e, portanto, mostra-se uma fundamentação matemática mais adequada. Ainda, o fato de que a teoria das categorias tem seu foco principalmente em relações melhor se relaciona à atenção primária presente na construção e representação de ontologias, que é orientada às relações entre os conceitos do domínio. Este trabalho parte destas motivações e formaliza ontologias como categorias de conceitos e relações conceituais. Subsequentemente são analisadas as construções categoriais presentes em ontologias e as consequências desta formalização para categorias de ontologias
A formal foundation for ontology alignment interaction models
Ontology alignment foundations are hard to find in the literature. The abstract nature of the topic and the diverse means of practice makes it difficult to capture it in a universal formal foundation. We argue that such a lack of formality hinders further development and convergence of practices, and in particular, prevents us from achieving greater levels of automation. In this article we present a formal foundation for ontology alignment that is based on interaction models between heterogeneous agents on the Semantic Web. We use the mathematical notion of information flow in a distributed system to ground our three hypotheses of enabling semantic interoperability and we use a motivating example throughout the article: how to progressively align two ontologies of research quality assessment through meaning coordination. We conclude the article with the presentation---in an executable specification language---of such an ontology-alignment interaction model
Managing Requirement Volatility in an Ontology-Driven Clinical LIMS Using Category Theory. International Journal of Telemedicine and Applications
Requirement volatility is an issue in software engineering in general, and in
Web-based clinical applications in particular, which often originates from an
incomplete knowledge of the domain of interest. With advances in the health
science, many features and functionalities need to be added to, or removed
from, existing software applications in the biomedical domain. At the same
time, the increasing complexity of biomedical systems makes them more difficult
to understand, and consequently it is more difficult to define their
requirements, which contributes considerably to their volatility. In this
paper, we present a novel agent-based approach for analyzing and managing
volatile and dynamic requirements in an ontology-driven laboratory information
management system (LIMS) designed for Web-based case reporting in medical
mycology. The proposed framework is empowered with ontologies and formalized
using category theory to provide a deep and common understanding of the
functional and nonfunctional requirement hierarchies and their interrelations,
and to trace the effects of a change on the conceptual framework.Comment: 36 Pages, 16 Figure
Interoperability in the OpenDreamKit Project: The Math-in-the-Middle Approach
OpenDreamKit --- "Open Digital Research Environment Toolkit for the
Advancement of Mathematics" --- is an H2020 EU Research Infrastructure project
that aims at supporting, over the period 2015--2019, the ecosystem of
open-source mathematical software systems. From that, OpenDreamKit will deliver
a flexible toolkit enabling research groups to set up Virtual Research
Environments, customised to meet the varied needs of research projects in pure
mathematics and applications.
An important step in the OpenDreamKit endeavor is to foster the
interoperability between a variety of systems, ranging from computer algebra
systems over mathematical databases to front-ends. This is the mission of the
integration work package (WP6). We report on experiments and future plans with
the \emph{Math-in-the-Middle} approach. This information architecture consists
in a central mathematical ontology that documents the domain and fixes a joint
vocabulary, combined with specifications of the functionalities of the various
systems. Interaction between systems can then be enriched by pivoting off this
information architecture.Comment: 15 pages, 7 figure
Using Ontologies for the Design of Data Warehouses
Obtaining an implementation of a data warehouse is a complex task that forces
designers to acquire wide knowledge of the domain, thus requiring a high level
of expertise and becoming it a prone-to-fail task. Based on our experience, we
have detected a set of situations we have faced up with in real-world projects
in which we believe that the use of ontologies will improve several aspects of
the design of data warehouses. The aim of this article is to describe several
shortcomings of current data warehouse design approaches and discuss the
benefit of using ontologies to overcome them. This work is a starting point for
discussing the convenience of using ontologies in data warehouse design.Comment: 15 pages, 2 figure
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