We give a semantical account of propositional identity which is stronger than mutual entailment. That is, according to our account: (1) if A = B is true in a model, so are A 'validates' B and B 'validates' A. (2) There exist models m such that A 'validates' B and B 'validates' A are true in m but A = B is not true in m. According to our account the following rule is sound: (3) from (.. A..) = (.. (...) B..) infer A = B. The paper respondes to a criticism of an earlier paper by James Freeman . (shrink)

Anderson and Belnap devise a model theory for entailment on which propositional identity equals proposional coentailment. This feature can be reasonably questioned. The authors devise two extensions of Anderson and Belnap’s model theory. Both systems preserve Anderson and Belnap’s results for entailment, but distinguish coentailment from identity.