1 Correction to: Synthese https://doi.org/10.1007/s11229-019-02474-5

The paragraph starting with “By accepting condition (a) only, ...” should be read as follows:

By accepting condition (a) only, one obtains an informational justification of a logic, the consequence relation of which deals with complete, but possibly inconsistent information. Note that the logic so defined is different from Priest’s Logic of Paradox. Indeed, in view of the second half of Definition 2.1 (and 2.2) dealing with negative information, and by the given assertion and denial conditions for negation, the former logic should employ a contrapositive negation (see the observation after Definition 2.1 about ‘preminimal’ negation). This is not the case for the Logic of Paradox, where \(A \models B \vee {\sim }B\) holds, but its contrapositive counterpart does not hold. To obtain an informational semantics of Priest’s logic, one should focus on positive information only and modify correspondingly Definitions 2.1 and 2.2, by omitting their second half. By taking into account only consistent position descriptions which need not be complete (condition (b) alone), one arrives at an informational semantics for a logic which deals with consistent, but possibly incomplete information. Again, to obtain an informational semantics of Kleene’s strong three-valued logic, one has to omit additionally the second half of Definitions 2.1 and 2.2. The possibility of such modifications opens the way to entailment relations which are sensitive to certain parts of the informational content of sentences, e.g., to the positive or negative information carried by them, or some combinations thereof.