Quantum view on contextual logic of composite intelligent devices

TL;DR

This paper introduces a quantum-inspired framework for analyzing the probabilistic logic of interconnected intelligent devices, highlighting the significance of indecomposable propositions for advanced logical processing.

Contribution

It proposes a novel quantum-based approach to study the probabilistic logic of composite intelligent systems, emphasizing the role of indecomposable propositions as a new logical resource.

Findings

Identified two classes of probabilistic propositions: decomposable and indecomposable.

Demonstrated that indecomposable propositions enable more powerful logical interactions.

Suggested applications in cognitive sciences, neuropsychology, and linguistics.

Abstract

Based on the ideas of quantum theory of open systems (QTOS) we propose the consistent approach to study probabilistic many-valued propositional logic of intelligent devices that are composed from separate but interconnected logical units. In this preliminary communication we consider only the simplest example of such systems, namely, four- valued probabilistic logical device composed of two logical subsystems. We demonstrate that similar devices can generate two classes of probabilistic propositions:1) decomposable propositions, which in fact are equivalent to certain ordered pair of propositions in device subsystems and 2) indecomposable propositions which are connected with inherent logical interaction between device units. The indecomposable propositions are undoubtedly of greatest interest since they, as shown in the paper, provide powerful additional logical resource compared to standard parallel processing in composite intelligent systems. The contextual logic of composite devices proposed in this paper, as we believe, can be also used for analysis of highly organized systems in cognitive sciences specifically in neuropsychology and linguistics.