https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=a5db01c09691ef6da94774aedb7aca037c0fcbff
Cafezeiro, I., Haeusler, E.H.: Semantic interoperability via category theory. In:
Conferences in Research and Practice in Information Technology, vol. 83 (2006)
Abstract
The paper uses categorical limit and colimit to define operations of breaking and composing ontologies, formalizing usual concepts in ontologies (alignment, merge, integration, matching) and proposing a new operation (the hide operation).
1 Introduction
In addition, restrictions are stated by the use of logical axioms given in some expressive language whose model-theoretic semantics provides meaning.
[Além de classes e propriedades Ontologias também tem regras mas não fala de instâncias]
Category Theory is an appropriate formal framework. First of all, because of the focus that is put in relationship (categorical morphisms) and not in entities (categorical object). In agreement with (i), entities are described abstractly, accordingly to their interactions with other entities. Secondly, it is possible to define several categories, according to the kinds of entities to be described. These categories can be related by the definition of relationships between categories (categorical functors) that preserve properties of categories. Thus, as stressed by (ii), it is possible for heterogeneous entities to coexist. Finally, addressing (iii), Category Theory offers a set of ways of combining entities, some of which (as colimits) are traditionally used to integrate entities.
[Justificativa para se basear em Teoria das Categorias para formalizar Ontologias Contextualizadas]
2 Categorical Theory, Limits and Colimits
In the above definition the notion of morphism is the central idea. It is asserted that morphisms have domain, codomain and a composition operation. In contrast, almost nothing is stated about objects. In general, the entity to be described is an object, but it is focused by an external view, given by means of morphisms.
[A forma é diferente da instância, a forma generaliza instâncias, é um modelo de um conjunto de instâncias]
3 Ontology Terminology
We are considering Maedche (2001), which presents ontologies in a layered approach composed of an ontology structure, a lexicon for the ontology structure, a knowledge base structure and a lexicon for the knowledge base structure.
[KB seriam instâncias?]
Ontology mapping is a total mapping from ontologies o1 to o2 which preserves hierarchy and conceptual relations and specify the semantic overlap between o1 and o2.
Ontology alignment “is the task of establishing a collection of binary relations between the vocabularies of two ontologies.
Ontology merging is the unification of two (or more) ontologies producing a new ontology that embodies the semantic differences and collapses the semantic intersection between the original ones.
Ontology matching is the task of finding commonalities between ontologies.
4 Ontologies in a Categorical View
4.1 Integration via Colimits
4.2 Integration via Limits
Th matching operation is important not only by its main purpose of detecting similarities, but also because in many frameworks it is part of the process of merging ontologies...
4.3 Limits for Hiding Information
5 Contextualizing Web Queries
Ontologies can be used to attach meaning to web pages. Using this semantic information, more accurate web consults can be implemented. The approach we describe here is to structure not only the web pages, but also the query themselves. We extend a given search algorithm to perform a pushout in a diagram composed by a contextualized query. In this way the search will result in ontologies that are semantically connected to the query. Morphisms from the query to results of the search give the semantic relationships.
[Ontologias para as consultas e para as páginas de resultado]
We informally define query as a textual description used to request for information in the Semantic Web. A query is always associated to a domain of knowledge over which we consider a context, defined by Jannink, J. et al (1998), as a unit of encapsulation for well-structured ontologies from which we are able to assert correctness and consistency properties. Finally, we name web consult the searching for information, on the Semantic Web, that is semantically related to the query.
[Diferença na definição de Contexto]
[Uma consulta está sempre associada a um domínio de conhecimento sobre o qual consideramos um contexto, definido por Jannink, J. et al (1998), como uma unidade de encapsulamento para ontologias bem estruturadas a partir das quais podemos afirmar propriedades de correção e consistência.]
[]
Describing queries by means of ontologies we are considering the possibility of having more sophisticated queries than unstructured textual information. Suppose also that a query is always linked to a context: an ontology (or a set of ontologies) that describes its domain of knowledge. Now, we can formally define query by establishing a connection between the ontology used to request for information and the (set of) ontology(ies) that compose the context. In this way, a query can be formally defined as a morphism in the category of ontologies.
[Uma query não seria somente texto e sim uma associação com uma ontologia de domínio e sua ontologia de contexto usada para uma operação de isomorfismo]
Definition 9 (Query) A query is a morphism in Ont, where the domain ontology is the information to be searched and the codomain ontology is the context of the query.
Cafezeiro, I., Viterbo, J., Rademaker, A., Haeusler, E.H., Endler, M. (2008). A Formal Framework for Modeling Context-Aware Behavior in Ubiquitous Computing. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation. ISoLA 2008. Communications in Computer and Information Science, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88479-8_37
Abstract.
The proposed algebra can be used to model applications in which the meaning of an entity depends on environment constraints or where dynamic changes in the environment have to be considered. In this article we use this algebra to formalize the problem of interpreting context information in ubiquitous systems, based on a concrete scenario.
[Computação Ubiqua ... o contexto da tarefa para identificar a entidade do mesmo conexto e não da alegação?]
1 Introduction
Despite that, until now, very few works can be found on formal models for this area, where the main challenge is to precisely model — and reason about — the interactions between a system and its environment, and the fact that this environment can change in unpredictable ways.
In particular, context-awareness, i.e. the ability of applications to detect changes in their environment and to adapt their behavior accordingly, has soon become the paramount programming paradigm for such systems.
[Contexto da tarefa]
[Se estou no topo do Himalaia e quero ferver água, ao perguntar qual é o ponto de ebulição da água a localização do dispositivo poderia completar a informação do contexto de localização e receber uma resposta exata]
[Se estou planejando uma viagem e quero conhecer a capital de um pais, o contexto temporal da aplicação de viagem onde realizo a busca por pontos turisticos pode considerar a capital atual. Mas se quero conhecer a história do pais pode ser interessante indicar pontos turisticos em cidades que já foram capitais anteriormente]
[Pode haver um contexto default no KG ou um contexto default na aplicação que é definido com informações do ambiente e pode ser usado para completar a consulta do usuário. Na {Best/All} Possible Answer esta "imputação" de contexto se torna explícita]
In [3] we have proposed a formal framework to contextualize ontologies, providing several ways of composing ontologies, contexts or both. This algebra is suitable for modeling applications in which the meaning of an entity depends on environment constraints or where dynamic changes in the environment should be considered. It emphasizes the relationships of contexts with entities — considering that contexts are essential to assign meaning to entities — and supports new forms of representing context for applications that consider dynamic changes of the environment.
[CKG, depois do paper WD, trata contexto da Alegações(Relações/Propriedades) e não das Entidades. Mas antes era possível associar Predicados com contextos de entidades]
2 Related Work
3 The Algebra of Contextualized Ontologies
The algebra of contextualized ontologies is designed for applications in which additional information is required in order to describe an entity. This information, that we call context, may be some kind of meta-data or any information related to — but not particular to — that entity.
[Contexto da Entidade e não da Alegação]
This is the case of ubiquitous computing applications [14]. Under this paradigm, information concerning either physical or computational environment is a relevant part of the application. Besides, the overall information available for an application — i.e. the context where it is imersed — constantly suffers dynamic changes.
[O Contexto da Alegação não muda. O Contexto da Consulta, quando preenchido pq o usuário sabe que existe contexto, pode variar uma vez que está associado a tarefa.]
This algebra is based on two basic features: (i) a uniform representation of entities and context and (ii) the emphasis on the relationship. Concerning (i), we use ontologies for representing both entities and contexts. This enhances the flexibility of the framework avoiding to determine a priori the role of an ontology: an ontology may represent an entity, a context or even both an entity and a context. Concerning (ii), the framework puts the focus on the relationship among the components of a systems and not on the components themselves. In this way, the internal constitution of an entity is hidden, and descriptions are built in a modular and reusable way.
[O mapeamento que compõe o CKG em termos de predicados x qualificadores]
3.1 Contextualized Ontologies
Contextualized Ontologies are described as structures that persist a link between two ontologies. The source of the link is the entity and the target is the context. By structure preserving we mean that the context respects the hierarchical structure and the ontological relations of the entity.
[O esquema do KG H estabalece quais são os predicados e qualificadores que podem ser usados. No CKG esta associação é relacionada (linkada) com um tipo de Contexto (ou dimensão contextual)]
Entity Integration. ... The result is a new entity (E) contextualized by the original ones (and by transitivity, by the original context CMed). The entity integration performs the semantic intersection of the entities under the mediation of the context, that is, the new entity will embody all, and nothing more than, information of the original entities that is mapped in the same component of the context.
Context Integration. ...
This operation can be used in situations where a single entity can be viewed in many ways, according to the considered context. The integration performs the amalgamated union of contexts, collapsing components that are images of the same component in the original entity.
4 Ubiquitous Computing
As a fundamental requirement, ubiquitous applications must be capable of responding to dynamic changes in their environments with minimal human interference. Users should be able to take full advantage of the local capabilities within a given environment and be able to seamlessly roam between several environments, despite variations of the computing and communication resources’ availability (e.g. available wireless bandwidth, residual energy, location-specific services, etc). Hence, ubiquitous computing systems strongly rely on context data, which is used to trigger adaptations at different levels, such as at communication protocols, middleware services, or the user interface.
[Exemplo, Caso de Uso. É parecido com o exemplo do ponto de ebulição da água pois trata de localização do usuário para realizar a tarefa, supondo que ele irá ferver a água no mesmo lugar onde ele faz a busca mas e a cauda longa?]
4.1 Scenario
From this example, we may see that the ubiquitous services described above rely on a wide variety of context information to trigger their actions. While the Ambient Management Service and the Personal Agenda must be aware of the context information that describes Silva’s role and location in the organization, the Configuration Management Service also takes into consideration Silva’s personal preferences.
[E se o Silva estiver remotamente acessando a Agenda? E se o Silva estiver remotamente operando um equipamento pela rede? E se o Silva estiver dando uma aula online? E se a intenção do Silva for se planejar para o dia de amanhã?]
5 Formalizing the Application
5.1 High Level Diagrams
5.2 A Zoom into Ontologies and Morphisms
The permission to print could be represented as a rule that would set an access permission in a ubiquitous regulation service, such as in [12]:
Person(?p) ∧ worksAt(?p,“PUC-Rio”) ∧ playsRole(?p,“Professor”) ⇒ hasAccess(?p,“Printer”)
[Regras de Acesso x Regras para inferir Contexto]
6 Conclusions
In this article, we used an algebra of contextualized ontologies to formalize the problem of interpreting context information in ubiquitous systems based on a concrete scenario.
Cafezeiro, I., Haeusler, E.H.: Semantic interoperability via category theory. In:
Conferences in Research and Practice in Information Technology, vol. 83 (2006)
Abstract
The paper uses categorical limit and colimit to define operations of breaking and composing ontologies, formalizing usual concepts in ontologies (alignment, merge, integration, matching) and proposing a new operation (the hide operation).
1 Introduction
In addition, restrictions are stated by the use of logical axioms given in some expressive language whose model-theoretic semantics provides meaning.
[Além de classes e propriedades Ontologias também tem regras mas não fala de instâncias]
Category Theory is an appropriate formal framework. First of all, because of the focus that is put in relationship (categorical morphisms) and not in entities (categorical object). In agreement with (i), entities are described abstractly, accordingly to their interactions with other entities. Secondly, it is possible to define several categories, according to the kinds of entities to be described. These categories can be related by the definition of relationships between categories (categorical functors) that preserve properties of categories. Thus, as stressed by (ii), it is possible for heterogeneous entities to coexist. Finally, addressing (iii), Category Theory offers a set of ways of combining entities, some of which (as colimits) are traditionally used to integrate entities.
[Justificativa para se basear em Teoria das Categorias para formalizar Ontologias Contextualizadas]
2 Categorical Theory, Limits and Colimits
In the above definition the notion of morphism is the central idea. It is asserted that morphisms have domain, codomain and a composition operation. In contrast, almost nothing is stated about objects. In general, the entity to be described is an object, but it is focused by an external view, given by means of morphisms.
[A forma é diferente da instância, a forma generaliza instâncias, é um modelo de um conjunto de instâncias]
3 Ontology Terminology
We are considering Maedche (2001), which presents ontologies in a layered approach composed of an ontology structure, a lexicon for the ontology structure, a knowledge base structure and a lexicon for the knowledge base structure.
[KB seriam instâncias?]
Ontology mapping is a total mapping from ontologies o1 to o2 which preserves hierarchy and conceptual relations and specify the semantic overlap between o1 and o2.
Ontology alignment “is the task of establishing a collection of binary relations between the vocabularies of two ontologies.
Ontology merging is the unification of two (or more) ontologies producing a new ontology that embodies the semantic differences and collapses the semantic intersection between the original ones.
Ontology matching is the task of finding commonalities between ontologies.
4 Ontologies in a Categorical View
4.1 Integration via Colimits
4.2 Integration via Limits
Th matching operation is important not only by its main purpose of detecting similarities, but also because in many frameworks it is part of the process of merging ontologies...
4.3 Limits for Hiding Information
5 Contextualizing Web Queries
Ontologies can be used to attach meaning to web pages. Using this semantic information, more accurate web consults can be implemented. The approach we describe here is to structure not only the web pages, but also the query themselves. We extend a given search algorithm to perform a pushout in a diagram composed by a contextualized query. In this way the search will result in ontologies that are semantically connected to the query. Morphisms from the query to results of the search give the semantic relationships.
[Ontologias para as consultas e para as páginas de resultado]
We informally define query as a textual description used to request for information in the Semantic Web. A query is always associated to a domain of knowledge over which we consider a context, defined by Jannink, J. et al (1998), as a unit of encapsulation for well-structured ontologies from which we are able to assert correctness and consistency properties. Finally, we name web consult the searching for information, on the Semantic Web, that is semantically related to the query.
[Diferença na definição de Contexto]
[Uma consulta está sempre associada a um domínio de conhecimento sobre o qual consideramos um contexto, definido por Jannink, J. et al (1998), como uma unidade de encapsulamento para ontologias bem estruturadas a partir das quais podemos afirmar propriedades de correção e consistência.]
[]
Describing queries by means of ontologies we are considering the possibility of having more sophisticated queries than unstructured textual information. Suppose also that a query is always linked to a context: an ontology (or a set of ontologies) that describes its domain of knowledge. Now, we can formally define query by establishing a connection between the ontology used to request for information and the (set of) ontology(ies) that compose the context. In this way, a query can be formally defined as a morphism in the category of ontologies.
[Uma query não seria somente texto e sim uma associação com uma ontologia de domínio e sua ontologia de contexto usada para uma operação de isomorfismo]
Definition 9 (Query) A query is a morphism in Ont, where the domain ontology is the information to be searched and the codomain ontology is the context of the query.
Cafezeiro, I., Viterbo, J., Rademaker, A., Haeusler, E.H., Endler, M. (2008). A Formal Framework for Modeling Context-Aware Behavior in Ubiquitous Computing. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation. ISoLA 2008. Communications in Computer and Information Science, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88479-8_37
Abstract.
The proposed algebra can be used to model applications in which the meaning of an entity depends on environment constraints or where dynamic changes in the environment have to be considered. In this article we use this algebra to formalize the problem of interpreting context information in ubiquitous systems, based on a concrete scenario.
[Computação Ubiqua ... o contexto da tarefa para identificar a entidade do mesmo conexto e não da alegação?]
1 Introduction
Despite that, until now, very few works can be found on formal models for this area, where the main challenge is to precisely model — and reason about — the interactions between a system and its environment, and the fact that this environment can change in unpredictable ways.
In particular, context-awareness, i.e. the ability of applications to detect changes in their environment and to adapt their behavior accordingly, has soon become the paramount programming paradigm for such systems.
[Contexto da tarefa]
[Se estou no topo do Himalaia e quero ferver água, ao perguntar qual é o ponto de ebulição da água a localização do dispositivo poderia completar a informação do contexto de localização e receber uma resposta exata]
[Se estou planejando uma viagem e quero conhecer a capital de um pais, o contexto temporal da aplicação de viagem onde realizo a busca por pontos turisticos pode considerar a capital atual. Mas se quero conhecer a história do pais pode ser interessante indicar pontos turisticos em cidades que já foram capitais anteriormente]
[Pode haver um contexto default no KG ou um contexto default na aplicação que é definido com informações do ambiente e pode ser usado para completar a consulta do usuário. Na {Best/All} Possible Answer esta "imputação" de contexto se torna explícita]
In [3] we have proposed a formal framework to contextualize ontologies, providing several ways of composing ontologies, contexts or both. This algebra is suitable for modeling applications in which the meaning of an entity depends on environment constraints or where dynamic changes in the environment should be considered. It emphasizes the relationships of contexts with entities — considering that contexts are essential to assign meaning to entities — and supports new forms of representing context for applications that consider dynamic changes of the environment.
[CKG, depois do paper WD, trata contexto da Alegações(Relações/Propriedades) e não das Entidades. Mas antes era possível associar Predicados com contextos de entidades]
2 Related Work
3 The Algebra of Contextualized Ontologies
The algebra of contextualized ontologies is designed for applications in which additional information is required in order to describe an entity. This information, that we call context, may be some kind of meta-data or any information related to — but not particular to — that entity.
[Contexto da Entidade e não da Alegação]
This is the case of ubiquitous computing applications [14]. Under this paradigm, information concerning either physical or computational environment is a relevant part of the application. Besides, the overall information available for an application — i.e. the context where it is imersed — constantly suffers dynamic changes.
[O Contexto da Alegação não muda. O Contexto da Consulta, quando preenchido pq o usuário sabe que existe contexto, pode variar uma vez que está associado a tarefa.]
This algebra is based on two basic features: (i) a uniform representation of entities and context and (ii) the emphasis on the relationship. Concerning (i), we use ontologies for representing both entities and contexts. This enhances the flexibility of the framework avoiding to determine a priori the role of an ontology: an ontology may represent an entity, a context or even both an entity and a context. Concerning (ii), the framework puts the focus on the relationship among the components of a systems and not on the components themselves. In this way, the internal constitution of an entity is hidden, and descriptions are built in a modular and reusable way.
[O mapeamento que compõe o CKG em termos de predicados x qualificadores]
3.1 Contextualized Ontologies
Contextualized Ontologies are described as structures that persist a link between two ontologies. The source of the link is the entity and the target is the context. By structure preserving we mean that the context respects the hierarchical structure and the ontological relations of the entity.
[O esquema do KG H estabalece quais são os predicados e qualificadores que podem ser usados. No CKG esta associação é relacionada (linkada) com um tipo de Contexto (ou dimensão contextual)]
Entity Integration. ... The result is a new entity (E) contextualized by the original ones (and by transitivity, by the original context CMed). The entity integration performs the semantic intersection of the entities under the mediation of the context, that is, the new entity will embody all, and nothing more than, information of the original entities that is mapped in the same component of the context.
Context Integration. ...
This operation can be used in situations where a single entity can be viewed in many ways, according to the considered context. The integration performs the amalgamated union of contexts, collapsing components that are images of the same component in the original entity.
4 Ubiquitous Computing
As a fundamental requirement, ubiquitous applications must be capable of responding to dynamic changes in their environments with minimal human interference. Users should be able to take full advantage of the local capabilities within a given environment and be able to seamlessly roam between several environments, despite variations of the computing and communication resources’ availability (e.g. available wireless bandwidth, residual energy, location-specific services, etc). Hence, ubiquitous computing systems strongly rely on context data, which is used to trigger adaptations at different levels, such as at communication protocols, middleware services, or the user interface.
[Exemplo, Caso de Uso. É parecido com o exemplo do ponto de ebulição da água pois trata de localização do usuário para realizar a tarefa, supondo que ele irá ferver a água no mesmo lugar onde ele faz a busca mas e a cauda longa?]
4.1 Scenario
From this example, we may see that the ubiquitous services described above rely on a wide variety of context information to trigger their actions. While the Ambient Management Service and the Personal Agenda must be aware of the context information that describes Silva’s role and location in the organization, the Configuration Management Service also takes into consideration Silva’s personal preferences.
[E se o Silva estiver remotamente acessando a Agenda? E se o Silva estiver remotamente operando um equipamento pela rede? E se o Silva estiver dando uma aula online? E se a intenção do Silva for se planejar para o dia de amanhã?]
5 Formalizing the Application
5.1 High Level Diagrams
5.2 A Zoom into Ontologies and Morphisms
The permission to print could be represented as a rule that would set an access permission in a ubiquitous regulation service, such as in [12]:
Person(?p) ∧ worksAt(?p,“PUC-Rio”) ∧ playsRole(?p,“Professor”) ⇒ hasAccess(?p,“Printer”)
[Regras de Acesso x Regras para inferir Contexto]
6 Conclusions
In this article, we used an algebra of contextualized ontologies to formalize the problem of interpreting context information in ubiquitous systems based on a concrete scenario.
Comentários
Postar um comentário
Sinta-se a vontade para comentar. Críticas construtivas são sempre bem vindas.