“…A lattice called an orthomodular lattice was developed not only for Boolean algebra but also for quantum logic (Birkhoff and von Neumann, 1936 ; Greechie, 1971 ; Maeda, 1980 ; Kalmbach, 1981 , 1983 ; Khrennikov, 2001 ). Since quantum mechanics is used as information science to explain decision-making and cognitive illusions (Khrennikov, 2001 , 2010 ; Aerts, 2009 ; Busemeyer and Bruza, 2012 ; Aerts et al, 2019 ; Ishwarya and Cherukuri, 2020 ), the way quantum logic is derived in cognition has recently been studied (Gunji and Haruna, 2022 ; Gunji and Nakamura, 2022a , b ). Lattice theory has also been developed in programming and computation to analyze programming (Scott, 1972 , 1976 ; Nielson et al, 2005 ).…”