We propose a model of unawareness that remains close to the paradigm of Aumann's model for knowledge [R. J. Aumann, International Journal of Game Theory 28 (1999) 263-300]: just as Aumann uses a correspondence on a state space to define an agent's knowledge operator on events, we use a correspondence on a state space to define an agent's awareness operator on events. This is made possible by three ideas. First, like the model of [A. Heifetz, M. Meier, and B. Schipper, Journal of Economic Theory 130 (2006) 78-94], ours is based on a space of partial specifications of the world, partially ordered by a relation of further specification or refinement, and the idea that agents may be aware of some coarser-grained specifications while unaware of some finer-grained specifications; however, our model is based on a different implementation of this idea, related to forcing in set theory. Second, we depart from a tradition in the literature, initiated by [S. Modica and A. Rustichini, Theory and Decision 37 (1994) 107-124] and adopted by Heifetz et al. and [J. Li, Journal of Economic Theory 144 (2009) 977-993], of taking awareness to be definable in terms of knowledge. Third, we show that the negative conclusion of a well-known impossibility theorem concerning unawareness in [Dekel, Lipman, and Rustichini, Econometrica 66 (1998) 159-173] can be escaped by a slight weakening of a key axiom. Together these points demonstrate that a correspondence on a partial-state space is sufficient to model unawareness of events. Indeed, we prove a representation theorem showing that any abstract Boolean algebra equipped with awareness, knowledge, and belief operators satisfying some plausible axioms is representable as the algebra of events arising from a partial-state space with awareness, knowledge, and belief correspondences.

翻译：我们提出了一种非完全认知模型，该模型在形式上接近Aumann的知识模型范式[R. J. Aumann, International Journal of Game Theory 28 (1999) 263-300]：正如Aumann利用状态空间上的对应关系来定义智能体在事件上的知识算子，我们利用状态空间上的对应关系来定义智能体在事件上的认知算子。这一构建基于三个关键思想。首先，与[A. Heifetz, M. Meier, and B. Schipper, Journal of Economic Theory 130 (2006) 78-94]的模型类似，我们的模型基于对世界进行部分描述的状态空间，这些部分描述通过进一步细化或精确化的关系形成偏序；智能体可能认知某些粗粒度描述，而对某些细粒度描述缺乏认知。然而，我们通过不同的数学实现方式来实现这一思想，该方法与集合论中的力迫法相关。其次，我们突破了由[S. Modica and A. Rustichini, Theory and Decision 37 (1994) 107-124]开创并被Heifetz等人及[J. Li, Journal of Economic Theory 144 (2009) 977-993]沿用的研究传统——该传统将认知定义为知识的衍生概念。第三，我们证明通过适度弱化[Dekel, Lipman, and Rustichini, Econometrica 66 (1998) 159-173]中关于非完全认知的著名不可能定理的关键公理，可以规避其否定性结论。这些要点共同表明：部分状态空间上的对应关系足以建模对事件的非完全认知。事实上，我们证明了一个表示定理：任何满足特定公理体系的、配备认知算子、知识算子和信念算子的抽象布尔代数，都可以表示为由具有认知对应、知识对应和信念对应的部分状态空间所生成的事件代数。