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Implication table, a tool used to facilitate the minimization of states in a state machine; Implication graph, a skew-symmetric directed graph used for analyzing complex Boolean expressions; Implication (information science)
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.
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 .
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, 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} .
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.