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Interplay Between Vertical and Horizontal Schemes of Computation: From Bayesian Inference to Quantum Logic via Gluing
Yukio-Pegio Gunji1, Kyoko Nakamura2, Kazuto Sasai3
1Department of Intermedia Art and Science, School of Fundamental Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan.
Entropy (Basel, Switzerland)
|May 26, 2026
Summary
This study introduces a new AI framework linking information processing with material embodiment. It reveals how dynamic reconfiguration of causal contexts naturally leads to quantum logic, advancing theories of open-ended computation.
Area of Science:
- Theoretical Computer Science
- Artificial Intelligence
- Computational Neuroscience
- Quantum Information Theory
Background:
- Current AI models often treat computation as fixed information processing, neglecting the material embodiment and continuous reconfiguration of biological systems.
- Existing frameworks struggle to unify fixed causal structures with the dynamic, evolving nature of real neural computation and learning.
- The reduction of computation to fixed causal structures fails to capture the adaptive and generative aspects of intelligence.
Purpose of the Study:
- To propose a theoretical framework unifying informational and material processes in computation.
- To formalize the interplay between fixed cause-effect relations (vertical scheme) and transformations of these relations (horizontal scheme).
- To demonstrate how this framework yields quantum logic from dynamically reconfiguring causal contexts.
Main Methods:
- Formulated a theoretical framework with two computational schemes: vertical (Bayesian inference) and horizontal (inverse Bayesian inference).
- Algebraically expressed the interaction between schemes as continuously gluing Boolean algebras.
- Demonstrated the emergence of a non-distributive orthomodular lattice (quantum logic) without Hilbert space formalism.
Main Results:
- The framework integrates Bayesian inference with inverse Bayesian inference, allowing for model space transformation.
- The algebraic construction yields a quantum logic structure from the dynamic reconfiguration of causal contexts.
- This approach provides a unified perspective on inference as both optimization and model generation/transformation.
Conclusions:
- The proposed framework offers a formal basis for understanding open-ended computation and embodied intelligence.
- It connects AI with unconventional computing and Natural Born Intelligence by emphasizing material interaction.
- Quantum logic emerges as a consequence of dynamic causal context reconfiguration, not from static assumptions.
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