Bibliography on Granularity/Granularité (2017-06-06)

Correspondences in ontology alignments relate two ontology entities with a relation. Typical relations are equivalence or subsumption. However, different systems may need different kinds of relations. We propose to use the concepts of algebra of relations in order to express the relations between ontology entities in a general way. We show the benefits in doing so in expressing disjunctive relations, merging alignments in different ways, amalgamating alignments with relations of different granularity, and composing alignments.

A temporal situation can be described at different levels of abstraction depending on the accuracy required or the available knowledge. Time granularity can be defined as the resolution power of the temporal qualification of a statement. Providing a formalism with the concept of time granularity makes it possible to model time information with respect to differently grained temporal domains. This does not merely mean that one can use different time units - e.g., months and days - to represent time quantities in a unique flat temporal model, but it involves more difficult semantic issues related to the problem of assigning a proper meaning to the association of statements with the different temporal domains of a layered temporal model and of switching from one domain to a coarser/finer one. Such an ability of providing and relating temporal representations at different "grain levels" of the same reality is both an interesting research theme and a major requirement for many applications (e.g. agent communication or integration of layered specifications). After a presentation of the general properties required by a multi-granular temporal formalism, we discuss the various issues and approaches to time granularity proposed in the literature. We focus on the main existing formalisms for representing and reasoning about quantitative and qualitative time granularity: the general set-theoretic framework for time granularity developed by Bettini et al and Montanari's metric and layered temporal logic for quantitative time granularity, and Euzenat's relational algebra granularity conversion operators for qualitative time granularity. The relationships between these systems and others are then explored. At the end, we briefly describe some applications exploiting time granularity, and we discuss related work on time granularity in the areas of formal specifications of real-time systems, temporal databases, and data mining.

Temporal and spatial phenomena can be seen at a more or less precise granularity, depending on the kind of perceivable details. As a consequence, the relationship between two objects may differ depending on the granularity considered. When merging representations of different granularity, this may raise problems. This paper presents general rules of granularity conversion in relation algebras. Granularity is considered independently of the specific relation algebra, by investigating operators for converting a representation from one granularity to another and presenting six constraints that they must satisfy. The constraints are shown to be independent and consistent and general results about the existence of such operators are provided. The constraints are used to generate the unique pairs of operators for converting qualitative temporal relationships (upward and downward) from one granularity to another. Then two fundamental constructors (product and weakening) are presented: they permit the generation of new qualitative systems (e.g. space algebra) from existing ones. They are shown to preserve most of the properties of granularity conversion operators.