Attention is the crucial cognitive ability that limits and selects what information we observe. Previous work by Bolander et al. (2016) proposes a model of attention based on dynamic epistemic logic (DEL) where agents are either fully attentive or not attentive at all. While introducing the realistic feature that inattentive agents believe nothing happens, the model does not represent the most essential aspect of attention: its selectivity. Here, we propose a generalization that allows for paying attention to subsets of atomic formulas. We introduce the corresponding logic for propositional attention, and show its axiomatization to be sound and complete. We then extend the framework to account for inattentive agents that, instead of assuming nothing happens, may default to a specific truth-value of what they failed to attend to (a sort of prior concerning the unattended atoms). This feature allows for a more cognitively plausible representation of the inattentional blindness phenomenon, where agents end up with false beliefs due to their failure to attend to conspicuous but unexpected events. Both versions of the model define attention-based learning through appropriate DEL event models based on a few and clear edge principles. While the size of such event models grow exponentially both with the number of agents and the number of atoms, we introduce a new logical language for describing event models syntactically and show that using this language our event models can be represented linearly in the number of agents and atoms. Furthermore, representing our event models using this language is achieved by a straightforward formalisation of the aforementioned edge principles.

翻译：注意是关键的认知能力，它限制并选择我们观察到的信息。Bolander等人（2016）的先前工作基于动态认知逻辑提出了一种注意模型，其中智能体要么完全注意，要么完全不注意。该模型虽然引入了不注意智能体认为“无事发生”这一现实特征，但未体现注意最本质的方面：其选择性。本文提出了一种泛化框架，允许智能体关注原子公式的子集。我们引入了相应的命题注意逻辑，并证明了其公理化的可靠性与完全性。随后，我们将该框架扩展至处理不注意智能体：这些智能体不假定“无事发生”，而是可能默认其未能注意到的信息具有特定真值（即一种关于未注意原子的先验假设）。这一特性使非注意盲视现象能得到更符合认知的刻画——智能体因未能注意突显但意外的事件而最终形成错误信念。两种模型版本均通过基于少量清晰边沿原则的动态认知逻辑事件模型定义了基于注意的学习机制。尽管这类事件模型的规模会随智能体数量和原子数量呈指数增长，但我们引入了一种用于语法描述事件模型的新逻辑语言，并证明使用该语言时，事件模型可表示为智能体与原子数量的线性形式。此外，通过直接形式化上述边沿原则即可实现用此语言对事件模型的表征。