A Galois-Connection between Cattell's and Szondi's Personality Profiles

TL;DR

This paper establishes a computable Galois-connection enabling automatic translation and interpretation between Cattell's 16PF personality profiles and Szondi's profiles, unifying two prominent personality measurement systems.

Contribution

It introduces a novel Galois-connection that allows for mutual interpretation and translation between Cattell's and Szondi's personality profiles, bridging their different psychometric frameworks.

Findings

Provides a pair of computable translations between the two personality spaces.

Enables automatic interpretation of personality test results.

Unifies depth psychology and trait theory through formal mathematical structures.

Abstract

We propose a computable Galois-connection between, on the one hand, Cattell's 16-Personality-Factor (16PF) Profiles, one of the most comprehensive and widely-used personality measures for non-psychiatric populations and their containing PsychEval Personality Profiles (PPPs) for psychiatric populations, and, on the other hand, Szondi's personality profiles (SPPs), a less well-known but, as we show, finer personality measure for psychiatric as well as non-psychiatric populations (conceived as a unification of the depth psychology of S. Freud, C.G. Jung, and A. Adler). The practical significance of our result is that our Galois-connection provides a pair of computable, interpreting translations between the two personality spaces of PPPs (containing the 16PFs) and SPPs: one concrete from PPP-space to SPP-space (because SPPs are finer than PPPs) and one abstract from SPP-space to PPP-space (because PPPs are coarser than SPPs). Thus Cattell's and Szondi's personality-test results are mutually interpretable and inter-translatable, even automatically by computers.