I will present an adaptive logic for the (monotonic) logic CLmin, the logic which underlies the goal directed proof procedure from [2], and which allows all classical consequences of a premise set to be derivable, except for those which where derived by means of the explosive “derivation rule” Ex Falso Quodlibet (see [1]). I will also point at the relations with Tennant’s relevantized classical logic CR (see [5] and [6]), and Besnard and Hunter’s quasi-classical logic QCL (see [3] and [4]). 1) Diderik Batens, “A paraconsistent proof procedure based on classical logic,” to appear. 2) Diderik Batens and Dagmar Provijn, “Pushing the search paths in the proofs. A study in proof heuristics,” Logique et Analyse, 173-174-175, 2001, pp. 113-134. (Appeared 2003) 3) Philippe Besnard and Anthony Hunter, “Quasi-classical logic: non-trivializable classical reasoning from inconsistent information.” In Froidevaux and Kohlas, editors, Symbolic and Quantitative Approaches to Uncertainty, Lecture Notes in Computer Science, vol. 946, Springer, 1995, pp. 44-51. 4) Anthony Hunter, “Reasoning with contradictory information using quasi-classical logic. Journal of Logic and Computation, vol. 10(5), 2000, pp. 677-703. 5) Neil Tennant, “Perfect validity, entailment and paraconsistency,” Studia Logica, vol. 18, 1984, pp. 181-200. 6) Neil Tennant, “Relevance in reasoning.” In Shapiro, editor, Handbook of Philosophical Logic and Mathematics, Oxford University Press, Oxford, 2004, pp. 696-726. 7) Guido Vanackere, “Minimizing ambiguity and paraconsistency,” Logique et Analyse, 165-166, 1999, pp. 139-160. (Appeared 2002)