The phrase "a logical proposition" is correct and usable in written English.
It can be used in contexts related to philosophy, mathematics, or formal logic when discussing statements that can be either true or false.
Example: "In formal logic, a logical proposition must be clearly defined to determine its truth value."
Alternatives: "a logical statement" or "a logical assertion".
That clearly makes no sense as a logical proposition.
In his famous proof, numbers carry two meanings — the familiar one designating a quantity, and an encoded one designating a logical proposition (e.g., "No number can be multiplied by 0 to produce 7").
A logical proposition is any proposition that can be reduced by replacement of its constituent terms to a proposition expressing a logical truth e.g., to a proposition such as "If p and q, then p".
As much as I might want to be sympathetic to this claim (I fly a lot and am wary of the "security theater" at American airports), it ought not to be very convincing as a logical proposition.
Unfortunately, not only did Basic Law V fail to be a logical proposition, but the resulting system proved to be inconsistent, for it was subject to Russell's Paradox.
However, in his two-volume work of 1893/1903, Grundgesetze der Arithmetik, Frege added (as an axiom) what he thought was a logical proposition (Basic Law V) and tried to derive the fundamental axioms and theorems of number theory from the resulting system.
For a complex logical proposition, however, such a definition may not be obvious, and a definition that provides an efficient architecture for implementing a logic circuit for the proposition is likely to be even more obscure.
Due to our requirement (v) above concerning Bolzano's replacement operation, neither an i-variant in general nor an is-variant in particular is defined for a purely logical proposition, since it does not contain any extra-logical idea.
But far from asking the corporation to act unlawfully, we have simply put forward a most logical proposition given the distinct lack of bi-partisanship for a very misguided policy.
Giving up requirement (v), as some would like to have it, results in a purely logical proposition being its only own is-variant.
Of course selling a Britney ticket to this [dance music] crowd is a much more logical proposition than trying to lure one to Celine or Elton".
