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    The claim conflates syntactic expressibility in SO-exists... — Carmelics
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    Challenges→NP is captured by the logic SO-exists (second-order existential logic)

    The claim conflates syntactic expressibility in SO-exists with semantic equivalence to NP, but expressibility results depend on the chosen encoding of problem instances as relational structures.

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    Key Terms

    NP (Nondeterministic Polynomial)(as used in computer science and logic)
    A class of computational problems whose solutions can be verified quickly, even if finding the solution is hard—like a Sudoku puzzle that's easy to check once solved.
    Relational structures(as the basis for understanding rights)
    Patterns of relationships between two or more things, where what matters is how they connect to and depend on each other.
    SO (Second-Order Logic)(as used in mathematical logic)
    A more powerful type of logical system that can talk not just about individual objects, but also about groups or properties of those objects.
    Syntactic(as used in linguistics)
    Related to the rules and structure of how words are arranged in language, rather than their meaning.
    encoding

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    (Contrasted with exemplification; characterized as 'internal' predication. E.g., the winged horse encodes the property winged without exemplifying it.)
    The mode of predication attributed to non-existent objects, by which such objects bear a property without instantiating it in the ordinary sense.
    expressibility(One of the logical capacities that the principles of a natural language account for)
    A logical capacity of a language to express a range of concepts and propositions
    semantic(describing the level of word meaning)
    Relating to the meaning of words and sentences.

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    Proof of definition segments1 linkedTruth & Knowledge1 linked

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    NP is captured by the logic SO-exists (second-order existential logic)

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