Classical foundations of quantum logic
- Univ. di Lecce (Italy)
The author constructs a language L for a classical first-order predicate calculus with monadic predicates only, extended by means of a family of statistical quantifiers. Then, a formal semantic model M is put forward for L which is compatible with a physical interpretation and embodies a truth theory which provides the statistical quantifiers with properties that fit their interpretation; in this framework, the truth mode of physical laws is suitably characterized and a probability-frequency correlation principle is established. By making use of L and M, a set of basic physical laws is stated that hold both in classical physics (CP) and in quantum physics (QP), which allow the selection of suitable subsets of primitive predicates of L and the introduction on these subsets of binary relations. Two languages L{sub E}{sup x} and L{sub E}{sup S} are constructed that can be mapped into L; the mapping induces on them mathematical structures, some kind of truth function, an interpretation. The formulas of L{sub E}{sup S} can be endowed with two different interpretations as statements about the frequency of some physical property in some class (state) of physical objects; consequently, a two-valued truth function and a multivalued fuzzy-truth function are defined on L{sub E}{sup S}. In all cases the algebras of propositions of these logics' are complete ortho-complemented lattices isomorphic to (E{sub E}, {prec}). These results hold both in CP and in QP; further physical assumptions endow the lattice (E{sub E}, {prec}), hence L{sub E}{sup x} and L{sub E}{sup s}, with further properties, such as distributivity in CP and weak modularity and covering law in QP. In the latter case, L{sub E}{sup x} and L{sub E}{sup s}, together with their interpretations, can be considered different models of the same basic mathematical structure, and can be identified with standard (elementary) quantum logics.
- OSTI ID:
- 7049542
- Journal Information:
- International Journal of Theoretical Physics; (United States), Journal Name: International Journal of Theoretical Physics; (United States) Vol. 30:1; ISSN 0020-7748; ISSN IJTPB
- Country of Publication:
- United States
- Language:
- English
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