Quantum Logic of Semantic Space: An Exploratory Investigation of Context Effects in Practical Reasoning

TL;DR

This paper explores how semantic space models, which are based on Hilbert spaces, can be used to formalize context effects in human reasoning, drawing parallels with quantum mechanics.

Contribution

It proposes a novel approach to model context effects in practical reasoning using the mathematical framework of quantum mechanics within semantic spaces.

Findings

Semantic space models are real-valued Hilbert spaces.

Quantum formalization offers a new perspective on context effects.

Operational issues in formalizing reasoning are discussed.

Abstract

This article is an exploratory account of the the non-monotonic behaviour of conceptual associations in the light of context. Computational approximations of conceptual space are furnished by semantic space models which are emerging from the fields of cognition and computational linguistics. Semantic space models not only provide a cognitively motivated basis to underpin human practical reasoning, but from a mathematical perspective, they are real-valued Hilbert spaces. This introduces the highly speculative prospect of formalizing aspects of human practical reasoning via quantum mechanics. This account focuses on how to formalize context effects in relation to concepts as well as keeping an eye on operational issues.