MONOTONICITY OF ENTAILMENT Meaning and
Definition
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Monotonicity of entailment refers to a property of logical reasoning in which the addition of new information to a set of premises does not invalidate or contradict any previously established conclusions or inferences. This property is essential in fields related to logic, such as mathematics, computer science, and philosophy.
In a logical system, entailment is the relationship between a set of premises and a conclusion that logically follows from those premises. By being monotonic, this relationship remains constant or strengthens as additional premises are introduced. In other words, if it is known that one statement entails another, then the addition of more premises should not reverse or eliminate this relationship.
The principle of monotonicity of entailment can be summarized as "what remains true, remains true." It ensures that logical conclusions are not affected by the inclusion of new information as long as the existing premises are still valid. This property allows for the cumulative development of knowledge and reasoning, as new facts and evidence can be incorporated without undermining previously established truths.
Monotonicity of entailment is a fundamental principle in various logical systems, including classical logic and many non-classical logics. It provides a measure of stability and reliability to logical reasoning, allowing for the growth and progression of knowledge without compromising the established truths.
