"Possible Definitions of an ’A Priori’ Granule\ud in General Rough Set Theory" by A. Mani

We introduce an abstract framework for general rough set theory from a mereological perspective and consider possible concepts of ’a priori’ granules and granulation in the same. The framework is ideal for relaxing many of the\ud relatively superfluous set-theoretic axioms and for improving the semantics of many relation based, cover-based and dialectical rough set theories. This is a\ud relatively simplified presentation of a section in three different recent research papers by the present author.\u

Ontology and medical terminology: Why description logics are not enough

Ontology is currently perceived as the solution of first resort for all problems related to biomedical terminology, and the use of description logics is seen as a minimal requirement on adequate ontology-based systems. Contrary to common conceptions, however, description logics alone are not able to prevent incorrect representations; this is because they do not come with a theory indicating what is computed by using them, just as classical arithmetic does not tell us anything about the entities that are added or subtracted. In this paper we shall show that ontology is indeed an essential part of any solution to the problems of medical terminology – but only if it is understood in the right sort of way. Ontological engineering, we shall argue, should in every case go hand in hand with a sound ontological theory

Algebraic, Topological, and Mereological Foundations of Existential Granules

In this research, new concepts of existential granules that determine themselves are invented, and are characterized from algebraic, topological, and mereological perspectives. Existential granules are those that determine themselves initially, and interact with their environment subsequently. Examples of the concept, such as those of granular balls, though inadequately defined, algorithmically established, and insufficiently theorized in earlier works by others, are already used in applications of rough sets and soft computing. It is shown that they fit into multiple theoretical frameworks (axiomatic, adaptive, and others) of granular computing. The characterization is intended for algorithm development, application to classification problems and possible mathematical foundations of generalizations of the approach. Additionally, many open problems are posed and directions provided.Comment: 15 Pages. Accepted IJCRS 202

A Theory of Granular Partitions

We have a variety of different ways of dividing up, classifying, mapping, sorting and listing the objects in reality. The theory of granular partitions presented here seeks to provide a general and unified basis for understanding such phenomena in formal terms that is more realistic than existing alternatives. Our theory has two orthogonal parts: the first is a theory of classification; it provides an account of partitions as cells and subcells; the second is a theory of reference or intentionality; it provides an account of how cells and subcells relate to objects in reality. We define a notion of well-formedness for partitions, and we give an account of what it means for a partition to project onto objects in reality. We continue by classifying partitions along three axes: (a) in terms of the degree of correspondence between partition cells and objects in reality; (b) in terms of the degree to which a partition represents the mereological structure of the domain it is projected onto; and (c) in terms of the degree of completeness with which a partition represents this domain

Spatio-structural granularity of biological material entities

<p>Abstract</p> <p>Background</p> <p>With the continuously increasing demands on knowledge- and data-management that databases have to meet, ontologies and the theories of granularity they use become more and more important. Unfortunately, currently used theories and schemes of granularity unnecessarily limit the performance of ontologies due to two shortcomings: (i) they do not allow the integration of multiple granularity perspectives into one granularity framework; (ii) they are not applicable to cumulative-constitutively organized material entities, which cover most of the biomedical material entities.</p> <p>Results</p> <p>The above mentioned shortcomings are responsible for the major inconsistencies in currently used spatio-structural granularity schemes. By using the Basic Formal Ontology (BFO) as a top-level ontology and Keet's general theory of granularity, a granularity framework is presented that is applicable to cumulative-constitutively organized material entities. It provides a scheme for granulating complex material entities into their constitutive and regional parts by integrating various compositional and spatial granularity perspectives. Within a scale dependent resolution perspective, it even allows distinguishing different types of representations of the same material entity. Within other scale dependent perspectives, which are based on specific types of measurements (e.g. weight, volume, etc.), the possibility of organizing instances of material entities independent of their parthood relations and only according to increasing measures is provided as well. All granularity perspectives are connected to one another through overcrossing granularity levels, together forming an integrated whole that uses the <it>compositional object perspective </it>as an integrating backbone. This granularity framework allows to consistently assign structural granularity values to all different types of material entities.</p> <p>Conclusions</p> <p>The here presented framework provides a spatio-structural granularity framework for all domain reference ontologies that model cumulative-constitutively organized material entities. With its multi-perspectives approach it allows querying an ontology stored in a database at one's own desired different levels of detail: The contents of a database can be organized according to diverse granularity perspectives, which in their turn provide different <it>views </it>on its content (i.e. data, knowledge), each organized into different levels of detail.</p