Completeness theorems for two propositional logics in which identity diverges from mutual entailment

Notre Dame Journal of Formal Logic 22 (3):269-282 (1981)
Abstract
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.
Keywords Anderson  Belnap  entailment  propositional identity
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C. Lewy (1964). Entailment And Propositional Identity. Proceedings of the Aristotelian Society 64:107-122.
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