This work builds upon a well-established research tradition on modal logics of awareness. One of its aims is to export tools and techniques to other areas within modal logic. To this end, we illustrate a number of significant bridges with abstract argumentation, justification logics, the epistemic logic of knowing-what and deontic logic, where basic notions and definitional concepts can be expressed in terms of the awareness operator combined with the box modality. Furthermore, these conceptual links point to interesting properties of awareness sets beyond those standardly assumed in awareness logics, i.e. positive and negative introspection. We show that the properties we list are characterised by corresponding canonical formulas, so as to obtain a series of off-the-shelf axiomatisations for them. As a second focus, we investigate the general dynamics of this framework by means of event models. Of specific interest in this context is to know under which conditions, given a model that satisfies some property, the update with an event model keeps it within the intended class. This is known as the closure problem in general dynamic epistemic logics. As a main contribution, we prove a number of closure theorems providing sufficient conditions for the preservation of our properties. Again, these results enable us to axiomatize our dynamic logics by means of reduction axioms.

翻译：本文建立在关于意识模态逻辑的成熟研究传统之上。其目标之一是将工具与技术拓展至模态逻辑的其他领域。为此，我们阐释了与抽象论证、辩护逻辑、知识之知的认知逻辑以及道义逻辑之间的若干重要桥梁——在这些领域中，基本概念与定义性概念可通过意识算子与必然模态算子的结合来表达。此外，这些概念联系揭示了意识集合中超越标准意识逻辑假设（即正内省与负内省）的有趣性质。我们证明所列举的性质可通过相应的正则公式刻画，从而获得一系列即用型公理化体系。第二个研究重点是借助事件模型探究该框架的一般动态规律。在此语境下，关键问题在于：给定满足某性质的模型，事件模型更新后是否仍能将该模型保持于目标类中——此即一般动态认知逻辑中的封闭性问题。作为主要贡献，我们证明了若干封闭性定理，为性质的保持提供了充分条件。这些结果同样使我们能够通过归约公理对动态逻辑进行公理化。