Epistemic logic is usually employed to model two aspects of a situation: the factual and the epistemic aspects. Truth, however, is not always attainable, and in many cases we are forced to reason only with whatever information is available to us. In this paper, we will explore a four-valued epistemic logic designed to deal with these situations, where agents have only knowledge about the available information (or evidence), which can be incomplete or conflicting, but not explicitly about facts. This layer of available information or evidence, which is the object of the agents’ knowledge, can be seen as a database. By adopting this sceptical posture in our semantics, we prepare the ground for logics where the notion of knowledge—or more appropriately, belief—is entirely based on evidence. The technical results include a set of reduction axioms for public announcements, correspondence proofs, and a complete tableau system. In summary, our contributions are twofold: on the one hand we present an intuition and possible application for many-valued modal logics, and on the other hand we develop a logic that models the dynamics of evidence in a simple and intuitively clear fashion.

中文翻译：

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四值动态认知逻辑

认知逻辑通常用于对情况的两个方面进行建模：事实方面和认知方面。然而，真理并不总是可以实现的，在许多情况下，我们被迫仅根据我们可以获得的任何信息进行推理。在本文中，我们将探索一种旨在处理这些情况的四值认知逻辑，其中代理仅了解可用信息（或证据），这些信息可能不完整或相互矛盾，但并不明确地了解事实。这一层可用的信息或证据，是代理知识的对象，可以看作是一个数据库。通过在我们的语义学中采用这种怀疑态度，我们为知识的概念——或者更恰当地说，信念——完全基于证据的逻辑奠定了基础。技术成果包括一套用于公告的约简公理、通信证明和完整的画面系统。总之，我们的贡献是双重的：一方面，我们提出了多值模态逻辑的直觉和可能的应用，另一方面，我们开发了一种逻辑，以简单直观的方式对证据的动态进行建模。