In this paper, we define the notion of genuinely non-traditional logics , and show that FDE is an easy example of such logics. Since some might find the (definable) arrow in FDE unsuitable to play the role of an implication, even for a non-reflexive logic, we consider some expansions of FDE with connectives satisfying more properties usually expected from implications.
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Cuenca et al. (2026) studied this question.
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