 I am grateful to Thomas Hendrey for drawing my attention (in 2011) to an error in the initial version of this entry, at a point in Section 2 after the formulation of the rules (∧I) and (∧E), where the discussion included the following: “Typically ⊢ will also be determined by many further classes of valuations (meaning: other than the class Val(⊢) of all valuations consistent with ⊢), various subsets of Val(⊢), but not so, as just remarked, in the present case.” By “the present case” was meant the case of ⊢ = ⊢∧. As Hendrey pointed out, this consequence relation is determined by numerous proper subsets of the set of all ∧-Boolean valuations, so the claim is false. In a moment of inattention I had confusingly passed from the correct thought that the only valuations consistent with ⊢∧ are the ∧-Boolean ones to the faulty conclusion that the only class of valuations determining ⊢∧ is the class of all ∧-Boolean valuations. (Many counterexamples could be given to this latter claim but one offered by Hendrey is particularly interesting: the class of all those ∧-Boolean valuations with the further property that they make at most one sentence letter false.) The reference to subsets of Val(⊢) was ill-conceived, since the point of contrast with, e.g., ⊢∨, taken as the consequence relation (on the language with sole connective ∨) determined by the class of all ∨-Boolean valuations is also determined by classes of valuations which are not subsets of this class since we can include also conjunctive combinations of ∨-Boolean valuations. By contrast, ⊢∧ can only be determined by classes of valuations all of which are ∧-Boolean. 