Logic, Mereology, classical and topological Geometries
Leśniewski's logical system is based on three formal components: Protothetic (a theory of relationships between propositions), Ontology (a logic of names), and Mereology (a general theory of part and whole). In these works, we deal with mereological reasoning and propose an interpretation of the above-mentioned system in terms of set theory, focusing, in particular, on the formalisation of the relation "part of". As a result, the package provides a specification of Mereology through the addition of two axioms .
In this paper we extend Clay's work to prove that mereology can be regarded as an atomless boolean algebra. The proof of this claim is achieved by providing an encoding of the axioms of mereology. Such encoding is done by embedding mereological axioms by using characteristic functions.