Monotonicity of Entailment

logic

Definition

Monotonicity of Entailment

Monotonicity of entailment is the property that adding antecedents does not remove existing consequents.

If a consequent $C$ follows from a set of antecedents $\Gamma$, then it also follows from any larger set of antecedents:

$$\Gamma ⊢C\Rightarrow \Gamma ,A⊢C$$

for any additional antecedent $A$.

In other words, valid arguments remain valid when extra assumptions are added. ¹

Footnotes

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