Summary |
Relevant logics are a group of logics which attempt to block irrelevant conclusions
being drawn from a set of premises. The following inferences are all valid in
classical logic, where A and B are any sentences whatsoever: from A to B → A, B → B and B ∨ ¬B; from ¬A to A→B; and from A ∧ ¬A to B. But if A and B are utterly irrelevant to one another, many feel reluctant to call
these inferences acceptable. Similarly for the validity of the corresponding material
implications, often called ‘paradoxes’ of material implication. Relevant logic can
be seen as the attempt to avoid these ‘paradoxes’. |