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  2. Sentence (mathematical logic) - Wikipedia

    en.wikipedia.org/wiki/Sentence_(mathematical_logic)

    In mathematical logic, a sentence (or closed formula) [1] of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition , something that must be true or false.

  3. Closed-form expression - Wikipedia

    en.wikipedia.org/wiki/Closed-form_expression

    The quadratic formula =. is a closed form of the solutions to the general quadratic equation + + =. More generally, in the context of polynomial equations, a closed form of a solution is a solution in radicals; that is, a closed-form expression for which the allowed functions are only n th-roots and field operations (+,,, /).

  4. Deductive closure - Wikipedia

    en.wikipedia.org/wiki/Deductive_closure

    Download as PDF; Printable version; ... ⁠ of logical formulae is deductively closed if it contains every formula ... In propositional logic, the set of all true ...

  5. Deduction theorem - Wikipedia

    en.wikipedia.org/wiki/Deduction_theorem

    The deduction theorem for predicate logic is similar, but comes with some extra constraints (that would for example be satisfied if is a closed formula). In general a deduction theorem needs to take into account all logical details of the theory under consideration, so each logical system technically needs its own deduction theorem, although ...

  6. Complete theory - Wikipedia

    en.wikipedia.org/wiki/Complete_theory

    In mathematical logic, a theory is complete if it is consistent and for every closed formula in the theory's language, either that formula or its negation is provable. That is, for every sentence φ , {\displaystyle \varphi ,} the theory T {\displaystyle T} contains the sentence or its negation but not both (that is, either T ⊢ φ ...

  7. Structure (mathematical logic) - Wikipedia

    en.wikipedia.org/wiki/Structure_(mathematical_logic)

    A subset | | of the domain of a structure is called closed if it is closed under the functions of , that is, if the following condition is satisfied: for every natural number , every -ary function symbol (in the signature of ) and all elements ,, …,, the result of applying to the -tuple … is again an element of : (,, …,).

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