Paraconsistent Informational Logic

We introduce a Paraconsistent Informational Logic that formalizes the idea of conjectures which are acceptable as to the quality and the variety of the information that they convey with respect to a given theory T, even if they are classically inconsistent with T. The work constitutes an extension of a previously developed Informational Logic for classical frameworks, where a new notion of logical entropy measure H on formulas and on proofs plays a central role.