Sequent logic of arithmetic decidability∗
نویسنده
چکیده
Our paper continues, on the one hand, the study of modal logics that have arithmetical semantics, and on the other, the investigation of decidability (or “non-contingency”) logics. We present Hilbert-style axiomatic system for the non-contingency logic of the Gödel-Löb provability logic GL, in other words, for the logic that is complete under the interpretation of a formula BA as ‘a sentence A is decidable in the Peano Arithmetic PA’. We also present sequent calculi for the non-contingency logics of K, K4, and GL.
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