On Quantic Conuclei in Orthomodular Lattices
Leopoldo Román, Rita Zuazua · Theory and applications of categories · 1996
. In this paper we study the lattice of conuclei for orthomodular lattices. We show that under certain conditions we can get a complete characterization of all quantic conuclei. The thing to note is that we use a non-commutative, non-associative disjunction operator which can be thought of as from non-commutative, non-associative linear logic. Introduction The purpose of this note is to begin the study of quantic conuclei in several lattices. Quantic conuclei were first introduced in [NR] and later were also introduced in the book [R] written by K. Rosenthal. The main motivation of our work is as follows. In [RR2] the first author and Beatriz Rumbos gave a complete description of the lattice of all quantic nuclei of an orthomodular lattice L. The first author knew the dual concept of a quantic nucleus but there was no obvious connection between quantic nucleus and quantic conucleus for orthomodular lattices. Since the birth of linear logic we know that dual properties could be useful ...