Studia Logica

, Volume 63, Issue 1, pp 7-25

First online:

An Operational Logic of Proofs with Positive and Negative Information

  • Duccio LuchiAffiliated withDipartimento di Matematica, University di Siena
  • , Franco MontagnaAffiliated withDipartimento di Matematica, University di Siena

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The logic of proofs was introduced by Artemov in order to analize the formalization of the concept of proof rather than the concept of provability. In this context, some operations on proofs play a very important role. In this paper, we investigate some very natural operations, paying attention not only to positive information, but also to negative information (i.e. information saying that something cannot be a proof). We give a formalization for a fragment of such a logic of proofs, and we prove that our fragment is complete and decidable.

provability logic logic of proofs proof theory