more from John P. Burgess

### Single Idea 15425

#### [catalogued under 5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi]

Full Idea

It might be wondered how one could have any kind of proof procedure at all if transitivity of entailment is disallowed, but the sequent calculus can get around the difficulty.

Gist of Idea

The sequent calculus makes it possible to have proof without transitivity of entailment

Source

John P. Burgess (Philosophical Logic [2009], 5.3)

Book Reference

Burgess,John P.: 'Philosophical Logic' [Princeton 2009], p.105

A Reaction

He gives examples where transitivity of entailment (so that you can build endless chains of deductions) might fail. This is the point of the 'cut free' version of sequent calculus, since the cut rule allows transitivity.