Justification Logic and Applications

论证逻辑和应用

• 批准号: 0830450
• 负责人: Sergei Artemov
• 金额: $ 37.5万
• 依托单位: CUNY Graduate School University Center
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0830450&HistoricalAwards=false
• 关键词: Justification; Logic; Applications

Artemov, Fitting, and Nogina will continue their development of Justification Logic, which offers a possible breakthrough in the quest to create a fundamental theory of knowledge, belief, and evidence, and has the potential for significant impact on applications. The celebrated account of knowledge as "justified true belief," which is attributed to Plato, has long been a focus of epistemic studies. About a half-century ago, the notions of knowledge and belief acquired formalization by means of modal logic. However the notion of justification, an essential element of epistemic studies, was conspicuously absent, and this led to well-known deficiencies inherent in modal logics of knowledge.Justification Logic extends the logic of knowledge in three major ways. First, it adds a long-anticipated mathematical notion of justification, making the logic more expressive. We now have the capacity to reason about justifications, simple and compound. We can compare different pieces of evidence pertaining to the same fact. We can measure the complexity of justifications, thus connecting the logic of knowledge to a rich complexity theory, etc. Second, justification logic furnishes a new, evidence-based foundation for the logic of knowledge, according to which `F is known' is interpreted as `F has an adequate justification.' Third, justification logic provides a novel, evidence-based mechanism of truth tracking which can be a valuable tool for extracting robust justifications from a larger body of justifications which are not necessarily reliable.Knowledge, belief, and evidence are fundamental concepts whose significance spans many areas of human activity: computer science and artificial intelligence, mathematics, economics and game theory, cryptography, philosophy, and other disciplines. Justification Logic promises significant impact on the aforementioned areas. In particular, the capacity to keep track of pieces of evidence, compare them, and select those that are appropriate would be a valuable new tool.

Artemov，Fitting和Nogina将继续他们的辩护逻辑的发展，这为寻求创造知识，信仰和证据的基础理论提供了可能的突破，并有可能对应用产生重大影响。柏拉图将知识描述为“被证明的真信念”，这一著名的观点一直是认识论研究的焦点。大约半个世纪以前，知识和信仰的概念通过模态逻辑获得了形式化。然而，作为认识论研究的一个基本要素，辩护的概念却明显缺失，这导致了知识模态逻辑中众所周知的固有缺陷。辩护逻辑在三个主要方面扩展了知识逻辑。 首先，它增加了一个期待已久的数学概念的理由，使逻辑更具表现力。我们现在有能力对简单和复杂的理由进行推理。我们可以比较与同一事实有关的不同证据。我们可以测量证明的复杂性，从而将知识逻辑与丰富的复杂性理论联系起来，等等。第二，证明逻辑为知识逻辑提供了一个新的、基于证据的基础，根据这个基础，“F是已知的”被解释为“F有充分的证明”。“第三，辩护逻辑提供了一种新颖的、以证据为基础的真理追踪机制，它可以成为一种有价值的工具，用于从大量不一定可靠的辩护中提取强有力的辩护。知识、信念和证据是基本概念，其意义跨越人类活动的许多领域：计算机科学与人工智能、数学、经济学与博弈论、密码学、哲学等学科。证明逻辑对上述领域有着重要的影响。特别是，跟踪、比较和选择适当证据的能力将是一个宝贵的新工具。