A P-lattice is a σ-complete, orthomodular atomic lattice ℒ which is formed by the set of propositions of a physical system. A composition of physical systems is considered, and some concept of locality in a compound physical system is represented in terms of P-lattices. We give a remark toward necessary and sufficient conditions for it to hold, which have been provided implicitly in antecedent studies, and we show that it can be provided under weaker conditions.

1.
S.
Kochen
and
E.
Specker
,
J. Math. Mech.
17
,
59
(
1967
).
2.
J. S.
Bell
,
Physics (Long Island City, N.Y.)
1
,
195
(
1964
).
3.
W. Demopoulos, in Studies in the Foundations of Quantum Mechanics, edited by P. Suppes (PSA, East Lansing, MI, 1980), pp. 119–144.
4.
T.
Matolcsi
,
Acta. Sci. Math. (Szeged)
37
,
263
(
1975
).
5.
D.
Aerts
and
I.
Daubechies
,
Helv. Phys. Acta
51
,
661
(
1978
).
6.
D. Aerts, in Current Issues in Quantum Logic, edited by E. G. Beltrametti and B. C. van Fraassen (Plenum, New York, 1981), pp. 381–403.
7.
A.
Stairs
,
Synthese
56
,
47
(
1983
).
8.
S.
Pulmannová
,
J. Math. Phys.
26
,
1
(
1985
).
9.
A.
Zecca
,
Int. J. Theor. Phys.
33
,
983
(
1994
).
10.
F. Valckenborgh, in Current Research in Operational Quantum Logic, edited by B. Coecke, D. Moore, and A. Wilce (Kluwer Academic, Dordrecht, 2000), pp. 219–244.
11.
J. M. Jauch, Foundations of Quantum Mechanics (Addison-Wesley, Reading, MA, 1968).
12.
F. Maeda and S. Maeda, Theory of Symmetric Lattices (Springer-Verlag, Berlin, 1970).
13.
D.
Aerts
,
J. Math. Phys.
25
,
1434
(
1984
).
14.
R. Sikorski, Boolean Algebras, 2nd ed. (Springer-Verlag, Berlin, 1964).
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