  The term proposition usually denotes in quantum mechanics (QM) an element of
(standard) quantum logic (QL). Within the orthodox interpretation of QM the
propositions of QL cannot be associated with sentences of a language stating
properties of individual samples of a physical system, since properties are
nonobjective in QM. This makes the interpretation of propositions
problematical. The difficulty can be removed by adopting the objective
interpretation of QM proposed by one of the authors (semantic realism, or SR,
interpretation). In this case, a unified perspective can be adopted for QM and
classical mechanics (CM), and a simple first order predicate calculus L(x) with
Tarskian semantics can be constructed such that one can associate a physical
proposition (i.e., a set of physical states) with every sentence of L(x). The
set $P^{f}$ of all physical propositions is partially ordered and contains a
subset $P^{f}_{T}$ of testable physical propositions whose order structure
depends on the criteria of testability established by the physical theory. In
particular, $P^{f}_{T}$ turns out to be a Boolean lattice in CM, while it can
be identified with QL in QM. Hence the propositions of QL can be associated
with sentences of L(x), or also with the sentences of a suitable quantum
language $L_{TQ}(x)$, and the structure of QL characterizes the notion of
testability in QM. One can then show that the notion of quantum truth does not
conflict with the classical notion of truth within this perspective.
Furthermore, the interpretation of QL propounded here proves to be equivalent
to a previous pragmatic interpretation worked out by one of the authors, and
can be embodied within a more general perspective which considers states as
first order predicates of a broader language with a Kripkean semantics.
