One issue with Bar-Hillel and Carnap’s account of semantic information is that it assigns maximal informativeness to contradictions, an issue that has been termed the Bar-Hillel-Carnap Paradox. What happens if we replace the underlying classical logic and probability with the paraconsistent LP (Logic of Paradox)? Does it resolve the Bar-Hillel-Carnap Paradox? Here is an investigation into the matter:
Paraconsistent Semantic Information