Embedding of posets into lattices in quantum logic |
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Authors: | Claudio Garola |
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Institution: | (1) Dipartimento di Fisica dell'Universitá, Lecce, Italy;(2) Istituto Nazionale Fisica Nucleare, Italy |
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Abstract: | It has been proposed that some posets of quantum logic could be embedded into lattices in order to recover the lattice structure avoiding the introduction of ad hoc axioms. We consider here the embedding
s of any posetS into the complete lattice
s of its closed ideals ( normal embedding ofS) and show that
s can be characterized (up to a lattice isomorphism) either by means of a density property or by means of a minimality property. Both of these suggest that the normal embedding satisfies some intuitive conditions which make it preferable with respect to other possible embeddings ofS. We consider the poset of all the effects associated to yes-no experiments and briefly comment on the application of the normal embedding in this case. The possibility of giving a physical interpretation to the elements of
is also discussed.Research sponsored by CNR and INFN (Italy). |
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