An Overview of the 1997 IQSA Meeting in Atlanta

Abstract

The International Quantum Structures Association (IQSA) met in Atlanta the week of October 12, 1997, principally to plan its 1998 biannual meeting. This was a historic meeting as it was the first to be held in the United States. As is its custom whenever its members assemble, scientific ideas were exchanged, not only informally, but also in the form of research papers presented formally to the group. Many of these papers have been written up for publication. Some of them have been published elsewhere; others are being modified and will eventually appear in an evolved form, but a representative portion of them were submitted to this journal, have survived the refereeing process, and are assembled here to be published together. The papers are fairly representative of IQSA’ s activities. They are loosely assembled into three clusters. The first consists of those papers which focus on the so-called orthomodular structures or closely related structures. These are the (sometimes partial) algebraic structures (in order of increasing generality): Boolean algebras, orthomodular lattices, orthomodular posets, orthoalgebras, and effect algebras. Cattaneo, Dalla Chiara, and Giuntini, working in the setting of effect algebras or their lexicomorphic cousins quantum-MV-algebras, delineate six notions of a sharp physical property.o They study the relationships among these notions and show, among other things, that these six notions collapse into one in an MV-algebra. Navara discusses a theorem that insures the existence of an orthomodular lattice (OML) with certain prespecified state space properties given that a certain quite weak structure exists with the same property. These weak structures are, in fact, weaker than all the orthomodular structures listed above. He therefore provides us with a simple means of showing that OMLs exist with certain state space properties.