Quantum aspects of high dimensional formal representation of conceptual spaces

TL;DR

This paper explores a high-dimensional formal model of conceptual spaces that integrates geometric and quantum approaches, aiming to better understand human cognition and consciousness through mathematical analysis and a constructive learning scenario.

Contribution

It introduces a novel high-dimensional formal representation combining geometric and quantum perspectives to model human cognition and consciousness.

Findings

The model exhibits quantum aspects in conceptual representation.

Demonstrates how the model can achieve cognition and consciousness.

Provides an algorithm for conceptual scaling in real-world scenarios.

Abstract

Human cognition is a complex process facilitated by the intricate architecture of human brain. However, human cognition is often reduced to quantum theory based events in principle because of their correlative conjectures for the purpose of analysis for reciprocal understanding. In this paper, we begin our analysis of human cognition via formal methods and proceed towards quantum theories. Human cognition often violate classic probabilities on which formal representation of conceptual spaces are built. Further, geometric representation of conceptual spaces proposed by Gardenfors discusses the underlying content but lacks a systematic approach (Gardenfors, 2000; Kitto et. al, 2012). However, the aforementioned views are not contradictory but different perspective with a gap towards sufficient understanding of human cognitive process. A comprehensive and systematic approach to model a relatively complex scenario can be addressed by vector space approach of conceptual spaces as discussed in literature. In this research, we have proposed an approach that uses both formal representation and Gardenfors geometric approach. The proposed model of high dimensional formal representation of conceptual space is mathematically analysed and inferred to exhibit quantum aspects. Also, the proposed model achieves cognition, in particular, consciousness. We have demonstrated this process of achieving consciousness with a constructive learning scenario. We have also proposed an algorithm for conceptual scaling of a real world scenario under different quality dimensions to obtain a conceptual scale.