Abstract
We present here some Boolean connexive logics (BCLs) that are intended to be connexive counterparts of selected Epstein’s content relationship logics (CRLs). The main motivation for analyzing such logics is to explain the notion of connexivity by means of the notion of content relationship. The article consists of two parts. In the first one, we focus on the syntactic analysis by means of axiomatic systems. The starting point for our syntactic considerations will be the smallest BCL and the smallest CRL. In the first part, we also identify axioms of Epstein’s logics that, together with the connexive principles, lead to contradiction. Moreover, we present some principles that will be equivalent to the connexive theses, but not to the content connexive theses we will propose. In the second part, we focus on the semantic analysis provided by relating- and set-assignment models. We define sound and complete relating semantics for all tested systems. We also indicate alternative relating models for the smallest BCL, which are not alternative models of the connexive counterparts of the considered CRLs. We provide a set-assignment semantics for some BCLs, giving thus a natural formalization of the content relationship understood either as content sharing or as content inclusion.
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Acknowledgements
We want to thank the anonymous referees for their most valuable comments. We also would like to thank Tomasz Jarmużek who provided valuable insights for this and related endeavors. Luis Estrada-González was supported by the PAPIIT project IG400422 and by a DGAPA-PASPA sabbatical Grant.
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Special Issue: Frontiers of Connexive Logic Edited by: Hitoshi Omori and Heinrich Wansing.
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Klonowski, M., Estrada-González, L. Boolean Connexive Logic and Content Relationship. Stud Logica 112, 207–248 (2024). https://doi.org/10.1007/s11225-023-10058-1
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DOI: https://doi.org/10.1007/s11225-023-10058-1