Abstract: The present paper studies two approaches to the expressiveness of propositional modal logics based on first-degree entailment logic, FDE. We first consider the basic FDE-based modal logic BK and certain systems in its vicinity, and then turn to some FDE-based modal logics in a richer vocabulary, including modal bilattice logic, MBL. On the one hand, model-theoretic proofs of the definability of connectives along the lines of [7] and [17] are given for various FDE-based modal logics. On the other hand, building on [10], expressibility is considered in terms of mutual faithful embeddability of one logic into another logic. A distinction is drawn between definitional equivalence, which is defined with respect to a pair of structural translations between two languages, and weak definitional equivalence, which is defined with respect to a weaker notion of translations. Moreover, the definitional equivalence of some FDE-based modal logics is proven, especially the definitional equivalence of MBL and a conservative extension of the logic BK2 × BK2, which underlines the central role played by BK among FDE-based modal logics. © 2019 by Nicolaus Copernicus University in Toruń

Cite: Odintsov S.P. , Skurt D. , Wansing H.
On definability of connectives and modal logics over FDE
In compilation Logic and Logical Philosophy. 2019. – C.631-659. DOI: 10.12775/LLP.2019.010 Scopus OpenAlex

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Scopus:	2-s2.0-85072960409
OpenAlex:	W2936033652

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