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On the 'in many cases' Modality: Tableaux, Decidability, Complexity, Variants

机译:关于“在许多情况下”的模式:Tableaux,可决策性,复杂性,变体

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摘要

The modality 'true in many cases' is used to handle non-classical patterns of reasoning, like 'probably φ is the case' or 'normally φ holds'. It is of interest in Knowledge Representation as it has found interesting applications in Epistemic Logic, 'Typicality' logics, and it also provides a foundation for defining 'normality' conditionals in Non-Monotonic Reasoning. In this paper we contribute to the study of this modality, providing results on the 'majority logic' Θ of V. Jauregui. The logic Θ captures a simple notion of 'a large number of cases', which has been independently introduced by K. Schlechta and appeared implicitly in earlier attempts to axiomatize the modality 'probably φ'. We provide a tableaux proof procedure for the logic Θ and prove its soundness and completeness with respect to the class of neighborhood semantics modelling 'large' sets of alternative situations. The tableaux-based decision procedure allows us to prove that the satisfiability problem for Θ is NP-complete. We discuss a more natural notion of 'large' sets which accurately captures 'clear majority' and we prove that it can be also used, at the high cost however of destroying the finite model property for the resulting logic. Then, we show how to extend our results in the logic of complete majority spaces, suited for applications where either a proposition or its negation (but not both) are to be considered 'true in many cases', a notion useful in epistemic logic.
机译:模态“在许多情况下为真”用于处理非经典的推理模式,例如“可能是这样”或“通常是”。它在知识表示中引起了兴趣,因为它在认知逻辑,“典型”逻辑中发现了有趣的应用,并且还为定义非单调推理中的“正常”条件提供了基础。在本文中,我们为V. Jauregui的“多数逻辑”Θ的研究做出了贡献。逻辑Θ捕捉了一个“大量案例”的简单概念,该概念已由K. Schlechta独立提出,并隐含在更早的公理化模式“可能是φ”的尝试中。我们为逻辑Θ提供了一种证明性的证明程序,并针对建模“大量”替代情况的邻域语义类别证明了其合理性和完整性。基于表格的决策程序使我们能够证明Θ的可满足性问题是NP完全的。我们讨论了一个更自然的“大”集概念,该概念可以准确地捕捉“明显多数”,并且证明它也可以使用,但代价是高昂的代价是破坏了所得逻辑的有限模型属性。然后,我们展示如何在完全多数空间的逻辑中扩展我们的结果,适用于在许多情况下将命题或其否定(但不能同时包含两者)视为“真实”的应用,这在认知逻辑中很有用。

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  • 来源
  • 会议地点 Ioannina(GR)
  • 作者单位

    Department of Computer Science and Technology University of Peloponnese End of Karaiskaki Street, 22 100 Tripolis, Greece;

    Graduate Programme in Logic, Algorithms and Computation (MPLA) Department of Mathematics, University of Athens Panepistimioupolis, 157 84 ILissia, Greece;

    Department of Computer Science and Engineering University of Ioannina P.O. Box 1186, 45110 Ioannina, Greece;

    Graduate Programme in Logic, Algorithms and Computation (MPLA) Department of Mathematics, University of Athens Panepistimioupolis, 157 84 ILissia, Greece;

  • 会议组织
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    default modality; majority modal logic; tableaux proof procedure;

    机译:默认模式;多数模态逻辑桌面证明程序;

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