Theoretical analysis demonstrates categoricity conditions for first-degree entailment and refutes prior non-classical propositions, clarifying formal model structures.
This paper concerns the categoricity problems, or Carnap’s problems, of some non-classical logics. I first review the categoricity theorems of LP and K3 proved by Tabakci (2024) and give a counterexample to a proposition in his paper. Then I prove some categoricity results of FDE and a theorem connecting that of FDE and those of LP and K3 . I also prove that FDE is categorical regarding the star models and that LP and K3 are not categorical regarding their star models.
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Chris Pang (2026) studied this question.
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