We analyze the premises of recent propositions to test local realism via th
e Bell inequalities using neutral kaons from Phi resonance decays as entang
led Einstein-Podolsky-Rosen pairs. We pay special attention to the derivati
on of the Bell inequalities, or related expressions, for unstable and oscil
lating kaon ''quasispin'' states and to the possibility of the actual ident
ification of these states through their associated decay modes. We discuss
an indirect method to extract probabilities to find these states by combini
ng experimental information with theoretical input. However, we still find
inconsistencies in previous derivations of the Bell inequalities. We show t
hat the identification of the quasispin states via their associated decay m
ode does not allow the free choice to perform different tests on them, a pr
operty which is crucial to establish the validity of any Bell inequality in
the context of local realism. In view of this we propose a different kind
of Bell inequality in which the free choice or adjustability of the experim
ental setup is guaranteed. We also show that the proposed inequalities are
violated by quantum mechanics. [S0556-2821(99)08219-3].