Three types of logical structure resulting from the trilemma of free will, determinism and locality.

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.