Justification Logic and Applications

阿尔特莫夫、菲廷和诺吉娜将继续他们的论证逻辑的发展，这为寻求创造知识、信念和证据的基本理论提供了一个可能的突破，并有可能对应用产生重大影响。柏拉图对知识的著名描述是“正当的真信念”，长期以来一直是认识论研究的焦点。大约半个世纪以前，知识和信念的概念通过模态逻辑获得形式化。然而，作为认识论研究的一个基本要素，证明的概念明显缺失，这导致了众所周知的知识模态逻辑固有的缺陷。证明逻辑从三个主要方面扩展了知识的逻辑。首先，它增加了人们期待已久的证明的数学概念，使逻辑更具表现力。我们现在有能力对理由进行推理，无论是简单的还是复杂的。我们可以比较关于同一事实的不同证据。我们可以测量证明的复杂性，从而将知识的逻辑与丰富的复杂性理论联系起来，等等。其次，论证逻辑为知识逻辑提供了一个新的、以证据为基础的基础，根据这个基础，“F是已知的”被解释为“F有充分的论证”。第三，论证逻辑提供了一种新颖的、基于证据的真理跟踪机制，它可以从大量不一定可靠的论证中提取有力的论证，这是一个有价值的工具。知识、信念和证据是基本概念，其重要性跨越了人类活动的许多领域：计算机科学和人工智能、数学、经济学和博弈论、密码学、哲学和其他学科。Justification Logic承诺对上述领域产生重大影响。特别是，追踪证据、比较证据并选择适当证据的能力将是一种有价值的新工具。

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.