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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.
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"
Susan is ambitious. If she loses at something, she's pretty downcast. and that Peter intended the hearer to activate this knowledge. Then this is an implicated premise. The hearer can now draw the contextual implications that +> Susan needs to be cheered up. +> Peter wants me to ring Susan and cheer her up.
The sun being above the horizon is a necessary condition for direct sunlight; but it is not a sufficient condition, as something else may be casting a shadow, e.g., the moon in the case of an eclipse. The assertion that Q is necessary for P is colloquially equivalent to "P cannot be true unless Q is true" or "if Q is false, then P is false".
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 .
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] It can be summarized as "P implies Q. P is true. Therefore, Q ...
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.
An implication A→B is simply a pair of sets A⊆M, B⊆M, where M is the set of attributes under consideration. A is the premise and B is the conclusion of the implication A→B . A set C respects the implication A→B when ¬(C⊆A) or C⊆B.