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Dynamic Epistemic Logic with justification.

机译:有理由的动态认知逻辑。

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摘要

Justification Logic is the study of a family of logics used to reason about justified true belief. Dynamic Epistemic Logic is the study of logics used to reason about communication and true belief. This dissertation is a first step in merging these two areas, in that it defines theories for a joint language in which we may reason about communication alongside justified true belief.;After some preliminary matters, we go through a comprehensive survey of Dynamic Epistemic Logic, which primes us for the work at the end of the text. We then move into the core work of the dissertation, where we introduce a number of extensions of existing languages and theories of Justification Logic. Our extensions are all based on the work of Sergei Artemov, who extended the language of propositional logic by the addition of formula-labeling terms. This extension allows us to take a term t and a formula ϕ and form the new formula t:ϕ. The terms have a derivation-compatible structure that allows us to view terms as evidence verifying the truth of the formulas they label, which provides us with a means for reasoning about justified true belief.;We look at extensions of these theories that allow us to reason about evidence admissibility: the new formula t ≫ ϕ lets us express that t is admissible as evidence for ϕ, by which we mean that t may be taken into account when considering the truth of ϕ, though t need not conclusively validate ϕ. A further extension adds a unary modal operator □ that we use to reason about alternative evidence possibilities.;Nominated extensions of the latter languages allow us to express a notion of dynamic evidence introduction, whereby we may introduce a term t as admissible as evidence for ϕ. These extensions lead us to the final chapter of the text, where we combine our various systems of Justification Logic with the framework of Dynamic Epistemic Logic. Such joint theories contribute to the ongoing work aiming to provide a better foundational account of the reasoning of computational social agents.
机译:证明逻辑是对用于推理证明合理信念的一系列逻辑的研究。动态认知逻辑是对用于推理交流和真实信念的逻辑的研究。本论文是融合这两个领域的第一步,它定义了一种联合语言的理论,在其中我们可以在合理的真实信念的基础上进行交流;在经过一些初步的研究之后,我们对动态认知逻辑进行了全面的调查,这使我们可以在本文结尾处进行工作。然后,我们进入论文的核心工作,在其中介绍现有语言和“证明逻辑”理论的许多扩展。我们的扩展全部基于Sergei Artemov的工作,他通过添加公式标签术语扩展了命题逻辑的语言。该扩展使我们可以采用项t和公式ϕ。并形成新公式t:ϕ。术语具有衍生兼容结构,使我们可以将术语视为证明所标记公式的真实性的证据,这为我们提供了对合理的真实信念进行推理的手段。;我们着眼于这些理论的扩展,使我们能够证据可采性的理由:新公式t≫ ϕ让我们表示t可以作为ϕ的证据,这意味着在考虑ϕ的真相时可以考虑t,尽管t不必最终验证ϕ。进一步的扩展增加了一元模态运算符□后一种语言的指定扩展名使我们能够表达动态证据引入的概念,从而可以引入术语t作为ϕ的证据可以接受。这些扩展将我们引向本文的最后一章,在此我们将各种证明逻辑系统与动态认知逻辑框架相结合。这样的联合理论有助于正在进行的工作,旨在为计算社会主体的推理提供更好的基础说明。

著录项

  • 作者

    Renne, Bryan.;

  • 作者单位

    City University of New York.;

  • 授予单位 City University of New York.;
  • 学科 Computer Science.
  • 学位 Ph.D.
  • 年度 2008
  • 页码 335 p.
  • 总页数 335
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 自动化技术、计算机技术;
  • 关键词

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