Focusing in Orthologic

Olivier Laurent (1, 2)

1 PLUME - Preuves et Langages
2 LIP - Laboratoire de l'Informatique du Parallélisme

We propose new sequent calculus systems for orthologic (also known as minimal quantum logic) which satisfy the cut elimination property. The first one is a simple system relying on the involutive status of negation. The second one incorporates the notion of focusing (coming from linear logic) to add constraints on proofs and to optimise proof search. We demonstrate how to take benefits from the new systems in automatic proof search for orthologic.

Mots clés: orthologic; focusing; minimal quantum logic; linear logic; automatic proof search; cut elimination

Domaines: Logique [math.LO]; Logique en informatique [cs.LO]

Olivier Laurent. Focusing in Orthologic. Logical Methods in Computer Science, 2017, 13 (3), pp.6. ⟨10.23638/LMCS-13(3:6)2017⟩. ⟨hal-01566869⟩