Foundations of Physics

, Volume 20, Issue 6, pp 651–665

Lattice theory, quadratic spaces, and quantum proposition systems


  • Robert Piziak
    • Department of MathematicsBaylor University
Part II. Invited Papers Dedicated To The Memory Of Charles H. Randall (1928–1987)

DOI: 10.1007/BF01889453

Cite this article as:
Piziak, R. Found Phys (1990) 20: 651. doi:10.1007/BF01889453


A quadratic space is a generalization of a Hilbert space. The geometry of certain kinds of subspaces (“closed,” “splitting,” etc.) is approached from the purely lattice theoretic point of view. In particular, theorems of Mackey and Kaplansky are given purely lattice theoretic proofs. Under certain conditions, the lattice of “closed” elements is a quantum proposition system (i.e., a complete orthomodular atomistic lattice with the covering property).

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© Plenum Publishing Corporation 1990