Computer-Aided Discovery and Categorisation of Personality Axioms

TL;DR

This paper introduces a novel computer-algebraic, order-theoretic framework using intuitionistic logic to automatically discover, categorize, and visualize personality axioms and theories from test data, linking invariance with mental health.

Contribution

It presents a new formal approach combining category theory and intuitionistic logic for the discovery and categorization of personality axioms from symbolic test data.

Findings

Automated generation of formal personality theories.

Diagrammatic visualization of personality categories.

Mathematical characterization of invariance in personality theories.

Abstract

We propose a computer-algebraic, order-theoretic framework based on intuitionistic logic for the computer-aided discovery of personality axioms from personality-test data and their mathematical categorisation into formal personality theories in the spirit of F.~Klein's Erlanger Programm for geometrical theories. As a result, formal personality theories can be automatically generated, diagrammatically visualised, and mathematically characterised in terms of categories of invariant-preserving transformations in the sense of Klein and category theory. Our personality theories and categories are induced by implicational invariants that are ground instances of intuitionistic implication, which we postulate as axioms. In our mindset, the essence of personality, and thus mental health and illness, is its invariance. The truth of these axioms is algorithmically extracted from histories of partially-ordered, symbolic data of observed behaviour. The personality-test data and the personality theories are related by a Galois-connection in our framework. As data format, we adopt the format of the symbolic values generated by the Szondi-test, a personality test based on L.~Szondi's unifying, depth-psychological theory of fate analysis.