##  [Deep Inference](/index.php/deep-inference) 

  ##  [Deep Inference](https://mathlogic.quantumdictionary.io/deep-inference-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/index.php/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A proof-theoretic framework in which inference rules may be applied at any depth inside logical expressions rather than only at the root; deep inference supports symmetric, local, and often more compact proof systems such as the Calculus of Structures.