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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.
Material conditional (also material implication), a logical connective and binary truth function typically interpreted as "If p, then q" Material implication (rule of inference), a logical rule of replacement; Implicational propositional calculus, a version of classical propositional calculus that uses only the material conditional connective
An erosion gully in Australia caused by rabbits, an unintended consequence of their introduction as game animals. In the social sciences, unintended consequences (sometimes unanticipated consequences or unforeseen consequences, more colloquially called knock-on effects) are outcomes of a purposeful action that are not intended or foreseen.
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.
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 .
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]
It is elusive, because the meaning of relevance appears to be difficult or impossible to capture within conventional logical systems. The obvious suggestion that q is relevant to p if q is implied by p breaks down because under standard definitions of material implication, a false proposition implies all other propositions. However though 'iron ...
The basic idea of relevant implication appears in medieval logic, and some pioneering work was done by Ackermann, [3] Moh, [4] and Church [5] in the 1950s. Drawing on them, Nuel Belnap and Alan Ross Anderson (with others) wrote the magnum opus of the subject, Entailment: The Logic of Relevance and Necessity in the 1970s (the second volume being ...