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Mereology is the theory of parthood relations. These relations pertain to part to whole, and part-to-part within a whole. This area of research is today some of the core topics of ontology and of conceptual modelling in computer science and artificial intelligence. The present paper addresses a number of relevant topics of this research field. First, the paper presents an overview on the main abstract mereological systems, axiomatized in first Order Logic (FOL). Second, basic relations between merelogy and set theory are discussed. This section is based mainly on the results of D. Lewis. Third, the paper is devoted to a systematic classification of merelogical systems. We present a partial classification of the consistent complete extensions of two theories, of the general extension mereology (GEM) including the second order variant, and of the classical merelogy CM. Then, we present some new systems which are extensions of the ground mereology M by introducing the notion of the tree-skeleton of a partial ordering. A complete and general description of the notion of whole and part which works for every situation seems to be impossible. Hence, we purpose a logical framework which allows to formally capture the main aspects of parts and wholes.

DOI: 10.1007/978-90-481-8845-1_3

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