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  2. First-order logic - Wikipedia

    en.wikipedia.org/wiki/First-order_logic

    First-order logic also satisfies several metalogical theorems that make it amenable to analysis in proof theory, such as the Löwenheim–Skolem theorem and the compactness theorem. First-order logic is the standard for the formalization of mathematics into axioms, and is studied in the foundations of mathematics.

  3. List of first-order theories - Wikipedia

    en.wikipedia.org/wiki/List_of_first-order_theories

    There are three common ways of handling this in first-order logic: Use first-order logic with two types. Use ordinary first-order logic, but add a new unary predicate "Set", where "Set(t)" means informally "t is a set". Use ordinary first-order logic, and instead of adding a new predicate to the language, treat "Set(t)" as an abbreviation for ...

  4. Law of identity - Wikipedia

    en.wikipedia.org/wiki/Law_of_identity

    In first-order logic with identity, identity is treated as a logical constant and its axioms are part of the logic itself. Under this convention, the law of identity is a logical truth. In first-order logic without identity, identity is treated as an interpretable predicate and its axioms are supplied by the

  5. Decidability of first-order theories of the real numbers

    en.wikipedia.org/wiki/Decidability_of_first...

    In mathematical logic, a first-order language of the real numbers is the set of all well-formed sentences of first-order logic that involve universal and existential quantifiers and logical combinations of equalities and inequalities of expressions over real variables.

  6. Thousands of Problems for Theorem Provers - Wikipedia

    en.wikipedia.org/wiki/Thousands_of_Problems_for...

    [2] [3] [4] Problems are expressed in a simple text-based format for first order logic or higher-order logic. [5] TPTP is used as the source of some problems in CASC . References

  7. First-order predicate - Wikipedia

    en.wikipedia.org/wiki/First-order_predicate

    In mathematical logic, a first-order predicate is a predicate that takes only individual(s) constants or variables as argument(s). [1] Compare second-order predicate and higher-order predicate . This is not to be confused with a one-place predicate or monad, which is a predicate that takes only one argument.

  8. Puzzle Your Brain: 30 Odd One Out Questions That’ll ... - AOL

    www.aol.com/lifestyle/odd-one-challenge-only...

    We’ve all been there - facing a tricky puzzle, staring at options that seem alike, and wondering which one just doesn’t belong. Now is your chance to put your observation and reasoning skills ...

  9. Term (logic) - Wikipedia

    en.wikipedia.org/wiki/Term_(logic)

    Left to right: tree structure of the term (n⋅(n+1))/2 and n⋅((n+1)/2) Given a set V of variable symbols, a set C of constant symbols and sets F n of n-ary function symbols, also called operator symbols, for each natural number n ≥ 1, the set of (unsorted first-order) terms T is recursively defined to be the smallest set with the following properties: [1]

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