Equipollence
Equipollence
A relation of equivalence between two propositions or propositional forms or symbols for these.
(a) Some writers, following the example of Galen, use it in the sense of material equivalence, i.e., having the same truth value.
(b) Others, following Apuleius, use it in a much more restricted sense such as that of strict equivalence or even reciprocal entailment. In the latter sense the relation holds when and only when the two sentences express the same fact. — C.A.B.
Carnap proposes a purely syntactical definition of equipollence by defining two sentences (or two classes of sentences) to be equipollent if they have the same class of non-valid consequences. See the article Valid. — A.C.