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

Yukio Pegio Gunji*, Kyoko Nakamura, Mai Minoura, Andrew Adamatzky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Article number104151
Publication statusPublished - 2020 Jul


  • Cognition
  • Decision making
  • Lattice theory
  • Non-locality
  • Rough set theory

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • General Biochemistry,Genetics and Molecular Biology
  • Applied Mathematics


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