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The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol → {\displaystyle \rightarrow } is interpreted as material implication, a formula P → Q {\displaystyle P\rightarrow Q} is true unless P {\displaystyle P} is true and Q {\displaystyle Q} is false.
Universal generalization / instantiation. Existential generalization / instantiation. In propositional logic, material implication[1][2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- or and ...
propositional logic, Boolean algebra, first-order logic. ⊥ {\displaystyle \bot } denotes a proposition that is always false. The symbol ⊥ may also refer to perpendicular lines. The proposition. ⊥ ∧ P {\displaystyle \bot \wedge P} is always false since at least one of the two is unconditionally false. ∀.
Logical biconditional. In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement " if and only if " (often abbreviated as " iff " [1]), where is known as the antecedent, and the ...
Strict conditional. In logic, a strict conditional (symbol: , or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of classical logic, combined with the necessity operator from modal logic. For any two propositions p and q, the formula p → q ...
The symbol for material implication signifies the proposition as a hypothetical, or the "if–then" form, e.g. "if P, then Q". The biconditional statement of the rule of transposition (↔) refers to the relation between hypothetical (→) propositions, with each proposition including an antecedent and consequential term.
Material nonimplication or abjunction (Latin ab = "away", junctio = "to join") is a term referring to a logic operation used in generic circuits and Boolean algebra. [1] It is the negation of material implication. That is to say that for any two propositions and , the material nonimplication from to is true if and only if the negation of the ...
The matrix for negation is Russell's, alongside of which is the matrix for material implication in the hand of Ludwig Wittgenstein. It is shown that an unpublished manuscript identified as composed by Peirce in 1893 includes a truth table matrix that is equivalent to the matrix for material implication discovered by John Shosky.