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[en] An well posed theory of nature is expected to determine the future of an observer uniquely from a given set of appropriate initial data. In the context of general relativity, this is ensured by Penrose’s strong cosmic censorship conjecture. But in recent years, several examples are found which suggest breakdown of the deterministic nature of the theory in Reissner-Nordström-de Sitter black holes under the influence of different fundamental fields. Nevertheless, the situation has been reassuring for the case of astrophysically meaningful Kerr–de Sitter black hole solutions which seems to respect the conjecture. However, the previous analyses were done considering only the effect of scalar fields. In this paper, we extend the study by considering Dirac fields in Kerr-de Sitter background and show that there exist a parameter space which does not respect the conjecture.