Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Many-sorted logic cannot be considered a proper (strict) extension of first-order logic

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Many-sorted logic has strictly greater expressive power than single-sorted FOL when sort predicates cannot be first-order definable in the intended structure.
      ?

      Think about whether this reason is strong or weak

    • 2.Wang (1952) and Oberschelp (1962) demonstrate that many-sorted logic captures distinctions between sort domains that require additional axioms or expanded signatures in single-sorted FOL to replicate.
      ?

      Think about whether this reason is strong or weak

    • 3.A logic that requires non-trivial translation overhead with signature expansion to simulate another logic's native expressiveness constitutes a genuine, not merely apparent, extension of that logic.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Lindström's theorem characterizes logics up to expressive equivalence over unrestricted signatures, but many-sorted logic operates over typed signatures that are not freely interchangeable with single-sorted ones.
      ?

      Think about whether this reason is strong or weak

    • 2.The Lindström-style collapse of many-sorted logic into FOL depends on encoding sorts as unary predicates, which presupposes a metatheoretic translation that alters the intended semantics of sort-partitioned domains.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Lindström (1969) proves that first-order logic is the strongest logic possessing simultaneously Compactness and Löwenheim-Skolem properties
      ?

      Think about whether this reason is strong or weak

    • 2.First-order logic is the strongest logic where Löwenheim-Skolem holds and its set of valid sentences is recursively enumerable
      ?

      Think about whether this reason is strong or weak

    • 3.Many-sorted logic also possesses these properties (Compactness and Löwenheim-Skolem) as corollaries of its completeness theorem
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.