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  2. Propositional formula - Wikipedia

    en.wikipedia.org/wiki/Propositional_formula

    In mathematics, a propositional formula is often more briefly referred to as a "proposition", but, more precisely, a propositional formula is not a proposition but a formal expression that denotes a proposition, a formal object under discussion, just like an expression such as "x + y" is not a value, but denotes a value. In some contexts ...

  3. Proposition - Wikipedia

    en.wikipedia.org/wiki/Proposition

    For instance, the proposition "two plus two equals four" is distinct on a Russellian account from the proposition "three plus three equals six". If propositions are sets of possible worlds, however, then all mathematical truths (and all other necessary truths) are the same set (the set of all possible worlds). [citation needed]

  4. Propositional calculus - Wikipedia

    en.wikipedia.org/wiki/Propositional_calculus

    The definition that "nothing else is a formula", given above as Definition 3, excludes any formula from the language which is not specifically required by the other definitions in the syntax. [37] In particular, it excludes infinitely long formulas from being well-formed .

  5. Propositional variable - Wikipedia

    en.wikipedia.org/wiki/Propositional_variable

    In mathematical logic, a propositional variable (also called a sentence letter, [1] sentential variable, or sentential letter) is an input variable (that can either be true or false) of a truth function. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher-order logics.

  6. Propositional function - Wikipedia

    en.wikipedia.org/wiki/Propositional_function

    In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (x) that is not defined or specified (thus being a free variable), which leaves the statement undetermined.

  7. Converse (logic) - Wikipedia

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

    In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. For the categorical proposition All S are P, the converse is All P are S. Either way, the truth of the converse is generally independent from that of ...

  8. Mathematical proof - Wikipedia

    en.wikipedia.org/wiki/Mathematical_proof

    The definition of a formal proof is intended to capture the concept of proofs as written in the practice of mathematics. The soundness of this definition amounts to the belief that a published proof can, in principle, be converted into a formal proof. However, outside the field of automated proof assistants, this is rarely done in practice.

  9. Antecedent (logic) - Wikipedia

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

    Antecedent and consequent are connected via logical connective to form a proposition. If is a man, then is mortal. " is a man" is the antecedent for this proposition while "is mortal" is the consequent of the proposition. If men have walked on the Moon, then I am the king of France.