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In A History of Ancient Philosophy, Karsten Friis Johansen claims that Chrysippus offers a theory of truth for conditionals that is a version of strict implicature and intensional semantics. However, it would seem to me that Diodorius Cronus' version is much closer to strict implicature than that of Chrysippus. This is evidenced by the fact that many authors cite the Diodorus version as an example of strict implicature without making a similar claim of Chrysippus. So, is Johansen mistaken?

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Your consideration is supported by Benson Mates, Stoic Logic (1953), page 47 :

Is Diodorean implication the so-called "strict implication" of C.I.Lewis? [...] For, according to Diodorus, whatever is true for all time is necessarily true; thus, any conditional which would satisfy his requirements for truth would also satisfy his requirements for necessary truth.

And see page 55 :

Chrysippus, with reference to the (material) conditional, "If anyone is born under the Dog Star, then he will not be drowned in the sea," recommends that it be expresed as a negated conjunction, "Not both: someone is born under the Dog Star and he will be drowned in the sea."

He recommends this, incidentally, so that people will not be misled into supposing that a true material conditional indicates a necessary connection in nature.

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