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Proof Theory for Positive Logic with Weak Negation
Studia Logica ( IF 0.7 ) Pub Date : 2019-07-24 , DOI: 10.1007/s11225-019-09869-y
Marta Bílková , Almudena Colacito

Proof-theoretic methods are developed for subsystems of Johansson's logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems. In particular, cut-free complete sequent calculi are introduced and used to provide a proof of the fact that the systems satisfy the Craig interpolation property. Alternative versions of the calculi are later obtained by means of an appropriate loop-checking history mechanism. Termination of the new calculi is proved, and used to conclude that the considered logical systems are PSPACE-complete.

中文翻译:

弱否定正逻辑的证明理论

证明理论方法是为 Johansson 逻辑的子系统开发的,这些子系统是通过用弱否定扩展直觉逻辑的肯定片段而获得的。这些方法被用来建立逻辑系统的属性。特别是,引入了无切割完全序贯演算,并用于提供系统满足 Craig 插值属性这一事实的证明。稍后通过适当的循环检查历史机制获得演算的替代版本。证明了新演算的终止,并用于得出所考虑的逻辑系统是 PSPACE 完备的结论。
更新日期:2019-07-24
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