Monotonicity of Entailment

logic

Definition

Monotonicity of Entailment

Monotonicity of entailment is a property of many logical systems such that if a sentence follows deductively from a given set of sentences then it also follows deductively from any superset of those sentences. A corollary is that if a given argument is deductively valid, it cannot become invalid by the addition of extra premises. ¹

Let $C$ be a conclusion and $\Gamma$ be a set of premises. Symbolically, if $\Gamma ⊢C$, then $\Gamma ,A⊢C$, where $A$ being an arbitrary additional premise.

Footnotes

1. https://en.wikipedia.org/wiki/Monotonicity_of_entailment ↩