The paper discusses Kripke's semantics for truth and establishes some facts about related proof-theories. Let C be the class of Kripke interpretations, based on any one of a number of standard 3-valued logics, L, in which the interpretation of the truth predicate, T, is a fixed-point. The paper suggests that this class may characterise truth as a logical constant. Let \(\vDash_ L\) be the notion of validity defined in terms of truth preservation forward and falsity preservation backwards in all members of C. The paper shows that if there is a Gentzen system, sound and complete with respect to L, then this, augmented by the rules: \(A\vdash T\), \(T\vdash A\), \(\neg A\vdash \neg T\), \(\neg T\vdash \neg A\) (and some structural rules), is sound and complete with respect to \(\vDash_ L\) (where \(\) is a name of A). It then goes on to give a cut-free Gentzen system and prove soundness and completeness with respect to \(\vDash_ L\), where L is the Kleene strong 3-valued logic. Interestingly, these result hold if there are no constraints as to whether or not non-sentences may be counted true. If we insist that non- sentences are all false or all truth-valueless then, as the paper shows, \(\vDash_ L\) is not compact, and hence not axiomatisable. Since any other treatment of non-sentences is somewhat odd, and the paper identifies the meaning of a logical constant with its rules of proof, this is a rather unwellcome consequence. For more general problems with Kripke's account of truth, see the review by \textit{G. Hellman}, J. Symb. Logic 50, 1068-1071 (1985).