In this paper the problems of recognizability and strongrecognizavility, perceptibility and strong perceptibility in extensions ofthe minimal Johansson logic J [1] are studied. These concepts wereintroduced in [2, 3, 4]. Although the intuitionistic logic Int is recognizableover J [2], the problem of its strong recognizability over J is not solved.Here we prove that Int is strong recognizable and strong perceptible overthe minimal pre-Heyting logic Od and the minimal well-composed logicJX. In addition, we prove the perceptibility of the formula F over JX. Itis unknown whether the logic J+F is recognizable over J.
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