Part-of relations, functionality and dependence

Abstract

International audienceThat language hosts a multiplicity of part-whole relations is largely accepted, but no complete formal account is currently available. We first show how most distinctions between part-whole relations can be explained by considering the ontological categories of the arguments. We then focus on "component-integral whole" (CIW), a most important but formally little-studied relation. The analysis of the functional concepts involved leads us to introduce lexical categories and to characterize a notion of functional dependence. On this basis, four cases of CIW are distinguished and formally defined. The contrastive acceptability of determinative compound nouns shows the linguistic relevance of these distinctions. Lastly, we show how the definitions provide a simple solution to the elusive issue of variable transitivity patterns

The Problem of Transitivity of Part-Whole Relations in Conceptual Modeling Revisited

“…In other words, they all contribute to the functionality (or the behavior) of the complex. According to [2], parthood relations between complexes represent, aside from the mereological relation itself, relations of functional dependence. Take the example of figure 2.…”

“…Parthood is a relation of fundamental importance from the cognitive and linguistic perspectives [1,2]. In conceptual modeling, part-whole relations have also been considered of substantial significance.…”

“…These formal theories provide an important starting point for the understanding and axiomatization of the notion of Part. Nonetheless, despite their importance, there are many controversial properties that they ascribed to the part-whole relation that cannot be accepted by cognitive and conceptual theories of parthood [2,4,5]. One of these controversial properties is the unrestricted transitivity of parthood.…”

“…However, there are many counter-examples in the literature of part-whole relations in which transitivity is not warranted by language or cognition. For instance: (i) Rio de Janeiro is part of Brazil and Brazil is part of the United Nations (UN), it is not the case that Rio de Janeiro is part of the UN; (ii) the heart is part of the musician, the musician is part of the orchestra, but the heart is not part of the orchestra [2,4].…”

“…Firstly, we build on a formal ontological analysis of relations [8] and on the pioneering theory of transitivity of linguistic functional parthood relations [2] to propose a formal theory and typology of partwhole relations between functional complexes. Secondly, we employ this theory to propose a number of visual patterns that can be used as a methodological support for the identification of contexts of transitivity for this mostly common type of partwhole relations in conceptual modeling.…”