A sequent system for the interpretability logic with the persistence axiom
نویسنده
چکیده
In [Sas01], it was given a cut-free sequent system for the smallest interpretability logic IL. He first gave a cut-free system for IK4, a sublogic of IL, whose ✄-free fragment is the modal logic K4. Here, using the method in [Sas01], we give sequent systems for the interpretability logic ILP obtained by adding the persistence axiom P : (p✄ q) ⊃ ✷(p✄ q) to IL and for the logic IK4+P obtained by adding P to IK4. We also prove a cut-elimination theorem for the system for IK4P.
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