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Reforming Takeuti's Quantum Set Theory to Satisfy De Morgan's Laws
Masanao Ozawa
In 1981, Takeuti introduced set theory based on quantum logic by constructing a model analogous to Boolean-valued models for Boolean logic. He defined the quantum logical truth val…
Quantum-like modeling in biology with open quantum systems and instruments
Irina Basieva, Andrei Khrennikov, Masanao Ozawa
We present the novel approach to mathematical modeling of information processes in biosystems. It explores the mathematical formalism and methodology of quantum theory, especially…
Modeling combination of question order effect, response replicability effect, and QQ-equality with quantum instruments
Masanao Ozawa, Andrei Khrennikov
We continue to analyze basic constraints on the human decision making from the viewpoint of quantum measurement theory (QMT). As it has been found, the conventional QMT based on th…
Neutron optical test of completeness of quantum root-mean-square errors
Stephan Sponar, Armin Danner, Masanao Ozawa +1
One of the major problems in quantum physics has been to generalize the classical root-mean-square error to quantum measurements to obtain an error measure satisfying both soundnes…
Violation of Heisenberg's error-disturbance relation by Stern-Gerlach measurements
Yuki Inoue, Masanao Ozawa
Although Heisenberg's uncertainty principle is represented by a rigorously proven relation about intrinsic indeterminacy in quantum states, Heisenberg's error-disturbance relation…
Quantum Set Theory: Transfer Principle and De Morgan's Laws
Masanao Ozawa
In quantum logic, introduced by Birkhoff and von Neumann, De Morgan's Laws play an important role in the projection-valued truth value assignment of observational propositions in q…