  We present GS (Guarded Successor), a novel decidable temporal logic with
several unique distinctive features. Among those, it allows infinitely many
data values that come not only with equality but with a somehow rich theory
too: the first-order theory of atomless Boolean algebras. The language also
distinguishes between inputs and outputs, and has a decision procedure for
determining whether for all inputs exist outputs, at each point of time.
Moreover, and maybe most surprisingly, the data values can be nothing but
sentences in GS itself. We also present a non-temporal fragment called NSO
(Nullary Second Order) that enjoys merely this last property. These results are
crucial necessary ingredients in any meaningful design of safe AI. Finally, all
those results are obtained from a novel treatment of the first-order theory of
atomless Boolean algebras.
