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    Strong completeness requires that every semantically vali... — Carmelics
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    Challenges→XL can have a strongly complete calculus

    Strong completeness requires that every semantically valid inference be derivable, but many-sorted logics with sort-restricted quantifiers can generate models where cross-sort inferences resist standard Henkin construction.

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    Key Terms

    Cross-sort inferences(in mathematical logic)
    Logical conclusions that try to connect or compare different categories (like mixing statements about animals with statements about numbers).
    Derivable(in logic)
    Able to be proven or worked out step-by-step using the formal rules of a logical system.
    Henkin construction(as used in mathematical logic)
    A specific mathematical technique (named after logician Leon Henkin) for building models or examples that prove certain logical systems work correctly.
    Many-sorted logics(in mathematical logic)
    A type of formal logic system that divides things into different categories or 'sorts' (like separating numbers from animals) rather than treating everything as the same kind of object.
    Semantically valid inference

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    (logic)
    A logical argument where the conclusion must be true whenever all the premises (starting assumptions) are true, based on what the words actually mean.
    Sort-restricted quantifiers(in mathematical logic)
    Logical symbols that let you make statements about specific categories only—like saying 'all animals' without accidentally including numbers.
    Strong completeness(Distinguished from weak completeness, which only concerns tautologies)
    If φ is a semantic consequence of Γ (Γ ⊨ φ), then φ is provable from Γ (Γ ⊢ φ)
    models(models of global democracy)
    idealized theoretical constructions designed to express the normative qualities of a democratic system as well as its constitutive institutions

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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

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    XL can have a strongly complete calculus

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