A Theory of Concepts and Their Combinations I: The Structure of the Sets of Contexts and Properties

TL;DR

This paper introduces a quantum-inspired formalism for modeling concepts, incorporating context, states, and properties within a lattice structure, to better understand how context influences concept typicality and property applicability.

Contribution

It develops a formal framework using the SCOP model to represent concepts with context-dependent states and properties, laying groundwork for a quantum-like mathematical theory of concept combinations.

Findings

Set of contexts and properties form a complete orthocomplemented lattice

Model captures how context influences concept typicality and property applicability

Prepares for a quantum Hilbert space approach to concept combination

Abstract

We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts (see quant-ph/0402205)