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Logical consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically follows from one or more statements.
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- P {\displaystyle P} or Q {\displaystyle Q} and that either form can replace the other in ...
Logical consequence (also entailment or logical implication), the relationship between statements that holds true when one logically "follows from" one or more others; Material conditional (also material implication), a logical connective and binary truth function typically interpreted as "If p, then q"
A subfield of linear logic focusing on the study of affine transformations and their implications in logical reasoning. affirmative proposition A proposition that asserts the truth of a statement, as opposed to negating it. [7] [8] [9] affirming the consequent A logical fallacy in which a conditional statement is incorrectly used to infer its ...
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.
In propositional logic, the logical implication is defined as follows: P implies Q if and only if the proposition not P or Q is a tautology. Hence modus ponens, [P ∧ (P → Q)] ⇒ Q, is a valid logical conclusion according to the definition of logical implication just stated. Demonstrating the logical implication simply translates into ...
In propositional logic, modus ponens (/ ˈ m oʊ d ə s ˈ p oʊ n ɛ n z /; MP), also known as modus ponendo ponens (from Latin 'mode that by affirming affirms'), [1] implication elimination, or affirming the antecedent, [2] is a deductive argument form and rule of inference. [3]
Such a logical connective as converse implication "" is actually the same as material conditional with swapped arguments; thus, the symbol for converse implication is redundant. In some logical calculi (notably, in classical logic ), certain essentially different compound statements are logically equivalent .