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Logical consequence (also entailment or 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 ...
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. If Peter intended the hearer to come to these implications, they are implicated conclusions. Implicated premises and conclusions are the two types of implicatures in the relevance theoretical sense. [51]
The first implication suggests that S is a sufficient condition for N, while the second implication suggests that S is a necessary condition for N. This is expressed as " S is necessary and sufficient for N ", " S if and only if N ", or S ⇔ N {\displaystyle S\Leftrightarrow N} .
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.
Using material implication, if John is not in London then (a) is true; whereas if he is in London then, because he is not in Paris, (b) is true. Either way, the conclusion that at least one of (a) or (b) is true is valid.
According to Rolling Stone and Deadline, the rap mogul’s lawyer, Alex Spiro, filed new paperwork on Monday, December 30, seeking to challenge a lawsuit accusing Jay-Z of rape because the alleged ...
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 'method of putting by placing'), [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 must ...