Mereology in Engineering and Computer Science

Abstract

Mereology as an alternative to naive/formal Set Theory, predominant in formalizations of mathematical and informatic theories, is especially suited to discussions of relations among mass things, e.g., collections of them or spatial objects like figures, solids, etc., but, it finds also essential applications in other areas of engineering and comp uter science like assembling and design, planning, data classification, reasoning by means of cognitive schemes and in many-agent systems. Our chapter aims at presenting specimens of the role mereology plays in all of these areas of research. Out of a vast accumulated knowledge and of a plethora of applications, we strive to extract a skeleton of basic facts and exemplary applications in order to convey to the reader the elegance of solutions employing tools of mereology. We begin with a discussion of principles of Mereology, by giving a fairly detailed account of the pioneering formalization by Stanislaw Lesniewski in Sect. 2, followed by an account of Mereology based on the notion of a connection in Sect. 3. These two sections give a foundation for further developments. An extension of Mereology called Rough Mereology, which may be regarded as Mereology fused in a sense with Fuzzy and Rough Set Theories, is discussed in Sect. 3. An important, both for theory and applications, topological ingredient of Mereology is brought to the reader attention in Sect. 4, and on it, the Part I, Foundations, closes. In Part II, devoted to applications, we discuss the notion of an artifact, along with artifact design and assembling, in Sect. 5 and Sect. 6 brings forth a discussion of the role of Mereology in Spatial Reasoning and its applications like descriptions of shape and orientation and spatial calculi like RCC. A related topic of Planning and Navigation by means of mereological tools is presented in Sect. 7 for autonomous mobile agents (robots), and, in Sect. 8 we give an account of applications of Mereology in Knowledge Engineering, centered on Mereological Granular Computing in synthesis of data classifiers. Finally, Sect. 9 gives an account of the mereological perceptron networks, reasoning in many-agent systems by mereological tools for fusion of knowledge, and an account of ideas for Mereological Granular Logics.