How can one defend free will against determinism? Since quantum mechanics entails non-locality, it enables the co-existence of free will and determinism. Is non-locality in cognition possible, or must quantum mechanics be rejected? Here, we define free will, determinism and locality in terms of a binary relation between objects and representations, and we verify that the three concepts constitute a trilemma. We also show that non-locality in cognition is naturally found in decision making without any assumption of quantum mechanics. Three kinds of relations result from the trilemma. By using a rough set lattice technique, the three kinds of relations can be transformed into three kinds of logical structures. Type I is a naive set theoretical logic or Boolean algebra (i.e., all possible combinations of binary yes-no responses). Type II comprises all possible combinations of various multiple values, such as for the symptoms of schizophrenia. Type III is a non-local disjoint union of multiple contexts. The type III structure can show how non-locality in cognition can lead to the co-existence of free will and determinism. Loss of non-locality could play an essential role in the malfunction of the separation and integration of the self and others.

一个人如何捍卫自由意志反对确定论？由于量子力学需要非局部性，因此它可以使自由意志与确定性并存。认知中是否可能存在非局部性，还是必须拒绝量子力学？在这里，我们根据对象与表示之间的二元关系来定义自由意志，确定性和局部性，并验证这三个概念构成了一个三难困境。我们还表明，认知的非局域性是在没有任何量子力学假设的情况下自然地在决策中发现的。三难关系产生三种关系。通过使用粗糙集格技术，可以将三种关系转换为三种逻辑结构。类型I是朴素集理论逻辑或布尔代数（即，二进制“是-否”响应的所有可能组合）。II型包括各种多个值的所有可能组合，例如精神分裂症的症状。类型III是多个上下文的非局部不相交的并集。III型结构可以显示认知中的非局部性如何导致自由意志与确定性的共存。非本地性的丧失可能在自我与他人的分离和整合失灵中起重要作用。