Non-Wellfounded Proof Theory For (Kleene+Action)(Algebras+Lattices)
Non-Wellfounded Proof Theory For (Kleene+Action)(Algebras+Lattices)
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（克莱恩行动）的非充分证明理论（代数格）
DOI：
10.4230/lipics.csl.2018.19
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
D. Pous
中科院分区：
文献类型：
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作者：
Anupam Das;D. Pous
我们证明了一个序列风格的固定系统的切割，该系统是合理的，对于克莱恩代数的方程理论，以及（潜在的）非蜿蜒的无限树。我们将这些结果扩展到具有满足和残差的系统，以类似的方式捕获“恒星连续”动作晶格。我们通过限制定期证明（带有剪切）来恢复所有动作晶格的方程理论 - 那些是有限图的展现的证据。
We prove cut-elimination for a sequent-style proof system which is sound and complete for the equational theory of Kleene algebra, and where proofs are (potentially) non-wellfounded infinite trees. We extend these results to systems with meets and residuals, capturing `star-continuous' action lattices in a similar way. We recover the equational theory of all action lattices by restricting to regular proofs (with cut) - those proofs that are unfoldings of finite graphs.