From Input/Output Logics to Conditional Logics via Sequents - with Provers
From Input/Output Logics to Conditional Logics via Sequents - with Provers
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通过序列从输入/输出逻辑到条件逻辑 - 使用证明器
DOI：
10.1007/978-3-030-86059-2_9
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Björn Lellmann
中科院分区：
文献类型：
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作者：
Björn Lellmann
我们考虑输入/输出逻辑系列中许多道义逻辑的无割序列演算。这些连续的演算提供了与某些条件逻辑的平面片段的对应关系。引入的两个演算是非标准的，因为它们包含不可推导性陈述，因此从纯粹的技术角度来看也很有趣。我们在扩展的序列框架中进一步模块化计算。扩展演算中的证明搜索是在 Prolog 中实现的，似乎为某些所考虑的逻辑提供了第一个自动推理系统。
We consider cut-free sequent calculi for a number of deontic logics from the family of Input/Output logics. These sequent calculi provide a correspondence to the flat fragment of certain conditional logics. Two of the introduced calculi are non-standard in that they include non-derivability statements, and hence are interesting also from a purely technical perspective. We further modularise the calculi in an extended sequent framework. Proof search in the extended calculi is implemented in Prolog, providing seemingly the first automated reasoning systems for some of the considered logics.