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Preconditionals

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arxiv 2402.02296 v4 pith:SNZEE5HH submitted 2024-02-03 math.LO

Wesley H. Holliday This is my paper · ORCID
classification math.LO
keywords preconditionalssemanticsrelationalaxiomaticbeyondboundedcallclass
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In recent work, we introduced a new semantics for conditionals, covering a large class of what we call preconditionals. In this paper, we undertake an axiomatic study of preconditionals and subclasses of preconditionals. We then prove that any bounded lattice equipped with a preconditional can be represented by a relational structure, suitably topologized, yielding a single relational semantics for conditional logics normally treated by different semantics, as well as generalizing beyond those semantics.

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  1. Fundamental Propositional Logic with Preconditional: Strong Completeness, Finite Model Property, and Modal Translations

    math.LO 2026-07 accept novelty 6.0 of 10

    Fundamental logic with a preconditional is strongly complete, has the finite model property, and embeds fully and faithfully into ortho-S4 and intuitionistic KTB.

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