Individual Determinacy and Identity Criteria in Ontology-Driven Information Systems - Leitura de Artigo

 

 

 

Abstract.

The idea that the real-world entities referred to by Information Systems are determinate and uniquely identifiable is a commonly held assumption in the fields of Software Engineering and Database Systems. The concept of identity is also a central topic in Formal Ontology, a discipline that finds application in the field of Information Systems through the use of Foundational Ontologies (FOs).

[Em KG tem um conceito de UNA e NUNA, ter somente um ou mais de um nó representando o mesmo objeto do mundo real ou o mesmo conceito com diferentes rótulos ]

This work proposes two distinct, but logically equivalent, formal characterizations of the notion of individual determinacy.

[Individual Determinacy seria o Contexto de Identidade dos Conceitos e Entidades envolvidos na Alegação?]

Finally, it also introduces a few concepts that are useful in the analysis of identity criteria for the individuals represented using a FO’s theory

Introduction

An information system (IS) can be seen as an “organized combination of people, hardware, software, communications networks, data resources and policies that stores, retrieves, transforms, and disseminates information in an organization” [1]. ... ISs manipulate only abstract references to real objects.

As such, their value depend on the effectiveness of those references: if we cannot determine their referents, the IS’s information becomes meaningless. Also, even if the determination of referents is a process executed by the IS user, and not by the IS itself, the later still needs to decided whether or not two references have the same referee.

[Quais seria as informações de contexto (ou então nem seria contexto) para que o usuário pudesse determinar quais objeto do mundo real(ou conceitos) uma determinada alegação está referenciando?]

[Como resolver a referência ao mesmo objeto do mundo real? Em uma busca exploratória usando um KG os IDs da entidades envolvidas podem ser recuperados mas estes seriam suficientes para o usuário compreender qual (quais) entidades ou objetos do mundo real estão sendo referenciados na alegação e/ou no contexto? No exemplo da relação "capital de", a alegação "Rio de Janeiro capital de Brasil" poderia recuperar o ID do nó do Rio de Janeiro, município, mas como o usuário poderia ter certeza de que não se trata do estado? É só uma questão de interface, ou seja, clicar no nó e recuperar todos os atributos e relações deste nó ou haveria um subconjunto de atributos / relações que poderia ser recuperado na composição da "melhor resposta possivel" para evitar esta navegação adicional e reduzir o overhead de informações que um usuário deve lidar ao realizar a busca exploratória?]

At the root of this problem is the customary way of analyzing the concept of Identity by means of identity criteria [9], i.e., predicates that can be used to determine whether or not two references to objects of a certain kind share the same referent.

[Identidade é formada por predicados que podem ser usados para determinar se duas referências a objetos tratam do mesmo objeto ou não]

Predicates like these, that rely on logical identity or in the identity of elements that do not represent genuine properties of objects (e.g., OIDs - object identifiers), cannot be considered descriptive accounts of identity criteria, since they provide no genuine information that helps us to understand the identity conditions of the objects analyzed under their scope.

[O ID do nó não seria adequado como critério de identificação do conceito / entidade pq não é uma propriedade genuína do nó]

Using this notion, we can say that an individual is determinate if there exists an individual identity criteria for x. This characterization of determinacy, although intuitive, suffers from the same issues pointed up above, i.e., it also admits non-informative predicates as evidence of the determinacy of an individual.

In this work we address these issues by proposing (1) a characterization of individual identity criteria that avoids non-informative predicates; (2) a logically equivalent characterization of determinacy that is defined in terms of the models themselves and that does not depend on a choice of formal language or of logical forms of predicates; (3) a collection of concepts that can guide the discovery of genuine identity criteria.

1. Background

Foundational Ontologies are systems of general concepts that are applicable across domains, providing a framework that can be used to ground conceptual models, in general, including domain-specific ontologies. FOs such as DOLCE [11], GFO [12], BFO [13] and UFO [4] provide polished and well-tested definitions for general and ubiquitous concepts such as objects, properties, relations, parthood, etc., allowing their users to focus on the concepts that are specific to the domain in consideration while avoiding conceptual pitfalls that have already been addressed by the FO’s theory.

[Ontologias Fundacionais - definição]

2. Contribution

2.1. Individual Determinacy

The objects human beings refer to as particulars are generally considered to be determinate, at least on a mesoscopic level. The fact that we can recognize an object among the other objects in the universe means that this object has a sufficiently number of properties and relationships that allows its identity to be determined. An object’s identifiability can be characterized as the existence of a predicate that is satisfied exactly by the element that represents the object in an individual structure and no other. For example, supposing that fingerprint patterns are unique properties of human beings, we might say that human beings are identifiable because it is possible to define, for each one, a definite description predicate that picks it by comparing fingerprints.

[Parte da premissa da existencia de um predicado que permita identificar a instância]

The following definitions provide an alternate characterization for the notion of determinacy, as a function of the set of isomorphisms of an individual structure. We say that an individual is determinate in an individual structure if it is impossible to exchange it with another individual without invalidating some fact about the individuals in the structure. Conversely, we consider an individual indeterminate if there is a way to permute it with another individual in such a way that no change can be perceived in the individual structure:

Definition 1 (Permutability). An individual x of an individual structure S is said to be permutable with another individual y if and only if there is an permutation of S, represented by an isomorphism of S into itself, that maps x to y.

[Para ser determinado precisa ser não permutável dentro da estrutura S, que no meu caso pode ser o conjunto de nós do KG]

Definition 2 (Individual determinacy). An individual x of a individual structure S is considered determinate if and only if all permutations of S preserve x, i.e. x cannot be swapped seamlessly with a distinct individual of S.

2.2. Individual Identity Criteria

The concept of identity criteria, also referred to as identity condition, is frequently used to characterize the notion of identity of objects of a certain kind.

[Qual predicado (ou quais predicados) de uma classe pode ser usado para identificar as instâncias]

By focusing in a single individual instead of a class, we can define the notion of an individual identity criteria of an individual x as a special definite description of x that singles out x in a particular structure, i.e., a predicate that is only satisfiable by x in that structure. The identity criteria that applies to all instances of a class can be seen as capturing a common pattern of individual identity criteria for its instances

Theorem 1 (Individual identity criteria existence implies determinacy). Given a individual structure S and an individual x of S, if there is a predicate P that satisfies the conditions in (5) for an individual identity criteria for x in S, then the individual x is determinate in x, as per (2).

Theorem 2 (Determinacy implies individual identity criteria definability). For every individual structure S and every individual x of S, if x is determinate in S then it is possible to define, using the Hilbert’s choice operator, a predicate that satisfies the conditions for an individual identity criteria for x in S.

Nevertheless, the relationship between the notion of individual determinacy and of identity criteria hints that the analysis of the ontological characteristics that allows an informative identity criteria for x to be expressed in the context of an individual structure S can be found by understanding what makes x non-permutable in S.

2.3. Anchors and Determination Contexts

... intuition that an individual is determinate if it cannot be exchanged seamlessly with another.

However, this definition does explain exactly what elements in the structure ensure the uniqueness of an individual, i.e. it does not explain what are the truthmakers that ground the determinacy of an individual. This section presents an alternate but logically equivalent characterization that is existential in form, in that it expresses determinacy as the existence of certain substructures of an individual structure that ground the determinacy of a certain individual. These substructures are called determination contexts and they are characterized by the existence of certain morphisms, called anchors.

[Contexto de Determinação]

2.3.1. Anchors and determinacy

Definition 3 (Anchor). If S and S′ are configurations of individuals, x is an individual of S and y is an individual of S′, with an injective morphism φ from S to S′ that maps x to y, such that all injective morphisms from S and S′ also map x to y, we say that φ is an anchor for y in S′, and that S is an anchoring structure for y in S′.

[É possívem mapear x em y mas as estruturas onde x e y pertencem precisam ter uma função de mapeamento]

2.3.2. Determination Contexts

Definition 4 (Substructure). We say that a individual structure S′ is a substructure of S if and only if there is an inclusion morphism φ between S and S′, where a morphism is considered an inclusion morphism if it is a morphism between a configuration and another configuration whose set of individuals is a superset of the set of individuals of the former.

[O mapeamento ocorre por S' ser subconjunto de S]

Definition 5 (Determination Context). We call an anchoring structure for x in S that is also a substructure of S a determination context for x.

Since the existence of an anchoring structure for x implies the existence of a determination context and since a determination context is itself an anchoring structure for x, the existence of a determination context for x in S is equivalent to the existence of an anchor for x in S and thus, by Theorem (4), the existence of determination contexts for x in S is logically equivalent to the determinacy of x in S.

For example, if either the DNA code or the fingerprint of a person x is sufficient to determine the identity of x in a context represented by a configuration S, there would exist at least two determination contexts for x, one consisting in x with its DNA code and another consisting in x with its fingerprint.

[Existe um Contexto de Determinação para cada chave única natural, a chave pode ser simples ou pode ser composta]

Definition 6 (Minimal Determination Context). A determination context S′ for x is considered minimal if no other context for x is also a proper substructure of S′.

Minimal determination contexts represent minimal sets of sufficient properties for the determination of x’s identity in S.

Using the notion of determination context, we can define the notions of weak and strong identification dependency between individuals in a configuration

Definition 7 (Weak Identification Dependency). We say that an individual x of S is weakly identification-dependent upon an individual y of S if and only if there exists a minimal determination context for x that contains y

Definition 8 (Strong Identification Dependency). We say that an individual x of S is strongly identification-dependent upon an individual y of S if and only if x is determinate in S and all determination contexts of x also includes y.

The relation of weak identification dependency can be used to identify possible elements for use in the definition of identity criteria, while the relation of strong identification dependency indicate elements that are necessary for the definition of an identity criteria of an individual, i.e. that must be included in any definition of an identity criteria for that individual.
The notion of strong identification-dependency is also transitive and symmetric, configuring a pre-order over determinate individuals of a configuration. This relation can be used to determine the set of individuals that are essential for the identification of the individuals in the configuration. This set can serve as a basis for producing identity criteria.

The concept of determination contexts can also be used to determine whether the identity of an individual is an intrinsic or an extrinsic property of that individual. An individual can be considered intrinsically determinate if there is at least one determination context for it that only includes itself (or only itself and its parts, moments, etc.). Conversely, it can be considered extrinsically determinate if all of its determination contexts contain other externally dependent object.

3. Applications

The concept of determinacy presented in this work presents an objective criteria to validate the assumption that the representation embedded in an IS is sufficiently rich to enable the identity of its represented objects to be determined.

This has a direct application during conceptual modeling: while investigating the domain and gathering examples of objects, properties and relationships, the conceptual modeler can validate this assumption by looking for non-trivial permutations in its sample data.

[O conceito de determinância pode ser verificado durante a modelagem de dados, testando a permutabilidade de instâncias]
[Chaves artificiais não seriam o suficiente. Chaves naturais deveriam estar presentes. ]

4. Final Considerations

This work presents a formal theory characterizing the notion of Individual Determinacy and its relation to the notion of Individual Identity Criteria.

This theory considers the determinacy of an individual in a representation of a portion of reality as its non-permutability with other individuals in that representation.

[Não é possível trocar X por Y pq a identidadade de X está determinada]

... definition for the notion of determinacy of an individual expressed as the existence of a determination context for that individual. This notion, in turn, plays two useful roles: it serves as truthmaker for the assertion that an individual is determinate; and it puts in evidence the elements of the individual structure that can be used to define identification criteria for that individual.

[Entender o conceito de Contexto de Determinação]