Matrix representation of Husserl's part-whole-foundation theory
After being axiomatized by S. Leśniewski and A. Tarski between 1916 and 1930 [cf. \textit{S. Leśniewski}, ``On the foundations of mathematics'', Topoi 2, 3-52 (1983) for an English translation], the theory of the part- whole relation has been a subject of intense research under the name of `mereology'. The first-order axiomatization in a language with two binary predicates of both the part-whole and the foundation relation, as suggested by \textit{E. Husserl} in his ``Logische Untersuchungen'' (1901), has been initiated by the second author [``A first-order axiom system for non-universal part-whole and foundation relations'', Essays in memory of Aron Gurwitsch (ed. Lester Embree), University Press of America, 463-483 (1983)] and is continued in this paper with a second aim of illustrating ``the use of Boolean matrices in representing the logical properties of one- and (mainly) two-place predicates over finite universes''. (Under the name of `incidence matrices' Boolean matrices have been used for the same purpose in finite projective geometry.)
scientific article; zbMATH DE number 4202229