  In this work we discuss logical structures related to indistinguishable
particles. Most of the framework used to develop these structures was presented
in [17, 28] and in [20, 14, 15, 16]. We use these structures and constructions
to discuss possible ontologies for identical parti-cles. In other words, we use
these structures in order to characterize the logical structure of quantum
systems for the case of indistinguishable particles, and draw possible
philosoph-ical implications. We also review some proposals available in the
literature which may be considered within the framework of the quantum logical
tradition regarding the problem of indistinguishability. Besides these
discussions and constructions, we advance novel technical results, namely, a
lattice theoretical structure for identical particles for the finite
dimensional case. This kind of approach was not present in the scarcely
literature of quantum logic and indistinguishable particles.
