  Suszko's Sentential Calculus with Identity SCI results from classical
propositional calculus CPC by adding a new connective $\equiv$ and axioms for
identity $\varphi\equiv\psi$ (which we interpret here as `propositional
identity'). We reformulate the original semantics of SCI in terms of Boolean
prealgebras establishing a connection to `hyperintensional semantics'.
Furthermore, we define a general framework of dualities between certain
SCI-theories and Lewis-style modal systems in the vicinity of S3. Suszko's
original approach to two SCI-theories corresponding to S4 and S5 can be
formulated as a special case. All these dualities rely particularly on the fact
that Lewis' `strict equivalence' is axiomatized by the SCI-principles of
`propositional identity'.
