The Logical Interpretation of the Lattice Lq
In this chapter, the lattice of subspaces of a Hilbert space is investigated with respect to its logical interpretation. In Section 2.1, we introduce the abstract lattice L q, which has as a model the lattice of subspaces of a Hilbert space, and we mention some interesting properties of this lattice. In Section 2.2, the relation of commensurability is defined, which is of special interest from a formal point of view as well as for the physical interpretation of L q. In addition to the operations already defined in L q, we introduce, in Section 2.3, a further operation, the material quasi-implication, the existence of which is of great importance for the logical interpretation of the lattice L q. Keeping these formal results in mind we shall consider in Section 2.4 the question of what kind of requirements must be fulfilled by a lattice in order that it be interpretable as a logical calculus.
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Notes and References
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