Logophoricity is a phenomenon of coreferentiality that is not covered by the classical Chomskyan Binding theory. Compare (i) and (ii):
(i) * Billi told us that Elisabeth had invited himselfi (ii) Billi told us that Elisabeth had invited Charles and himselfi
In (i) himself cannot be bound by Bill (due to Condition A of the Binding theory). But in (ii) himself can be coreferential with Bill in (apparent) violation of Condition A. The co-referentiality of (ii) is considered one of logophoricity.
The notion arose in the 1990s in discussions of English himself. it was inspired by the phenomenon of logophoric pronouns, which were first described for African languages.