哥德尔逻辑的关系序列演算中的切消

M. Baaz, A. Ciabattoni, C. Fermüller
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引用次数: 24

摘要

在此之前,已经介绍了哥德尔逻辑的解析演算RG/sub /spl infin//。RG/sub /spl infin//操作的是“关系序列”。我们建设性地展示了如何从RG/sub /spl infin//-衍生中消除切割。我们考虑的切割规则的版本允许导出其他形式的切割以及对应于Avron的G/sub /spl infin//的超序演算的“通信规则”的规则。此外,我们给出了RG/sub /spl的所有公理的显式描述,并证明了它们的完备性。
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Cut-elimination in a sequents-of-relations calculus for Godel logic
Previously, the analytic calculus RG/sub /spl infin// for Godel logic has been introduced. RG/sub /spl infin// operates on "sequents of relations". We show constructively how to eliminate cuts from RG/sub /spl infin//-derivations. The version of the cut rule we consider allows to derive other forms of cut as well as a rule corresponding to the "communication rule" of Avron's hypersequent calculus for G/sub /spl infin//. Moreover, we give an explicit description of all the axioms of RG/sub /spl infin// and prove their completeness.
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