Mereological Algebras As Mechanisms For Reasoning About Sounds
Rita Singh, Carnegie Mellon University

Abstract:
This paper suggests the use and debates the appropriateness of Mereology for the study of real world sounds. Mereology is a formalism in mathematical logic that describes the universe in terms of parts and the wholes that are formed by the parts. This is in contrast with set theory, within which the universe is described as objects and the groups they belong to. Classification and traditional machine learning fit well into the description of the universe as a set of objects and their associated properties. In the case of sound, however, pieces of sound can extend and morph in time and frequency to form other recognizable sound entities without having clear partitions in the set theoretic sense. Our reasoning is that by treating sounds as composed entirely or parts, and wholes that are formed by parts, it may become easier to formalize the descriptions, mathematical manipulations and real-world interpretations for the universe of sounds. This paper is neither an exhaustive thesis on this subject, nor does it establish any formal system of Mereology for sound. The goal of this paper is to merely show that there are some promising possibilities with existing Mereological formalisms for manipulating the world of sounds differently, and perhaps more easily.