Proving Structural Properties of Sequent Systems in Rewriting Logic
General and effective methods are required for providing good automation strategies to prove properties of sequent systems. Structural properties such as admissibility, invertibility, and permutability of rules are crucial in proof theory, and they can be used for proving other key properties such as cut-elimination. However, finding proofs for these properties requires inductive reasoning over the provability relation, which is often quite elaborated, exponentially exhaustive, and error prone. This paper aims at developing automatic techniques for proving structural properties of sequent systems. The proposed techniques are presented in the rewriting logic metalogical framework, and use rewrite- and narrowing-based reasoning. They have been fully mechanized in Maude and achieve a great degree of automation when used on several sequent systems, including intuitionistic and classical logics, linear logic, and normal modal logics.
The authors would like to thank the anonymous reviewers for their valuable comments on an earlier draft of this paper. The work of the three authors was supported by CAPES, Colciencias, and INRIA via the STIC AmSud project “EPIC: EPistemic Interactive Concurrency” (Proc. No 88881.117603/2016-01). The work of Pimentel and Olarte was also supported by CNPq and the project FWF START Y544-N23.
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