Titlebook: Hiroakira Ono on Substructural Logics; Nikolaos Galatos,Kazushige Terui Book 2022 The Editor(s) (if applicable) and The Author(s), under e

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A Negative Solution to Ono’s Problem P52: Existence and Disjunction Properties in Intermediate Prediis an “abnormal” axiom, it plays an important role in our construction. We also introduce a condition (.) that excludes this “abnormal” . and is a natural condition for reasonable logics. We show that EP implies DP for .-normal logics. This result suggests a reason why Ono’s problem . has remained open.

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Recognizability in Residuated Latticesnizable element of . by a finite module and provide a characterization of such an element in the spirit of Myhill’s characterization of recognizable languages. Further, we investigate the structure of the set of recognizable elements of . and also provide sufficient conditions for a recognizable element to be recognized by a Boolean module.

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