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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. Logic translation - Wikipedia

   en.wikipedia.org/wiki/Logic_translation

   A logic translation is a translation of a text into a logical system.For example, translating the sentence "all skyscrapers are tall" as (() ()) is a logic translation that expresses an English language sentence in the logical system known as first-order logic.

4. Gödel numbering - Wikipedia

   en.wikipedia.org/wiki/Gödel_numbering

   In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. Kurt Gödel developed the concept for the proof of his incompleteness theorems .

5. Syntax (logic) - Wikipedia

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

   In logic, syntax is anything having to do with formal languages or formal systems without regard to any interpretation or meaning given to them. Syntax is concerned with the rules used for constructing, or transforming the symbols and words of a language, as contrasted with the semantics of a language which is concerned with its meaning.

6. Propositional formula - Wikipedia

   en.wikipedia.org/wiki/Propositional_formula

   A propositional formula may also be called a propositional expression, a sentence, [1] or a sentential formula. A propositional formula is constructed from simple propositions , such as "five is greater than three" or propositional variables such as p and q , using connectives or logical operators such as NOT, AND, OR, or IMPLIES; for example:

7. If and only if - Wikipedia

   en.wikipedia.org/wiki/If_and_only_if

   The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...

8. Well-formed formula - Wikipedia

   en.wikipedia.org/wiki/Well-formed_formula

   A closed formula, also ground formula or sentence, is a formula in which there are no free occurrences of any variable. If A is a formula of a first-order language in which the variables v 1, …, v n have free occurrences, then A preceded by ∀v 1 ⋯ ∀v n is a universal closure of A.

9. Independence-friendly logic - Wikipedia

   en.wikipedia.org/wiki/Independence-friendly_logic

   Independence-friendly logic is translation equivalent, at the level of sentences, with a number of other logical systems based on team semantics, such as dependence logic, dependence-friendly logic, exclusion logic and independence logic; with the exception of the latter, IF logic is known to be equiexpressive to these logics also at the level ...