OpenPsi: A Novel Computational Affective Model and Its Application in Video Games

Authors: Zhenhua Cai, Ben Goertzel, Changle Zhou, Deheng Huang, Shujing Ke, Gino Yu, Min Jiang
Year: 2013 (received 2011-12-22, revised 2012-06-10, accepted 2012-07-31, available online 2012-08-16)
Venue: Engineering Applications of Artificial Intelligence, Vol. 26, Issue 1, pp. 1--12
DOI: 10.1016/j.engappai.2012.07.013
RawData: RawData+Publications+Openpsi Zhenhua (chunk-1, chunk-2)

Summary

Introduces OpenPsi, a computational affective model formalizing part of Dietrich Doerner's PSI theory. Demands generate urges that drive intentions; modulators (Activation, Resolution Level, Securing Threshold, Selection Threshold) parameterize cognition; emotions emerge as regions in a multidimensional space spanned by demands and modulators. The model is implemented as six interacting "mind agents" (PerceptionUpdater, MonitorChanges, ActionSelection, DemandUpdater, ModulatorUpdater, FeelingUpdater) running on top of a shared AtomSpace knowledge base. Emotion emergence is verified via three Minecraft-inspired scenarios; phase transitions (trigger, self-amplification, self-stabilization) consistent with Lewis's dynamic theory of emotions are observed.

Key Equations

The paper's mathematical core is equations (1)--(17). Selected core formulas anchored by the OpenPsi cluster pilot Source 3 reconciliation (2026-04-28):

• Eq (1) Demand satisfaction (piecewise fuzzy): S_d(L, min_l, max_l, a)
• Eq (2) Fuzzy equality: fuzzy_equal(x, t, a) = 1 / (1 + a*(x-t)^2)
• Eq (5) Certainty level: L_certainty = (sum(fuzzy_new(t_i,t_s)) + rand) / ((1+exp(-0.05*n))*(n+1))
• Eq (6) fuzzy_new(t_i,t_s) = 2 / (1+exp(0.002*(t_s-t_i)))
• Eq (7) Competence: L_competence = n_s / (n_s + n_f^{3/2})
• Eq (8) Affiliation: L_affiliation = (sum(fuzzy_near(d_i,d_max)) + rand) / ((1+exp(-0.1*n))*(n+1))
• Eq (9) fuzzy_near(d_i,d_max) = 1 / (1 + 0.00015*(d_i-d_max))
• Eq (10) Activation: S_comp/(S_comp+0.5) * S_en/(S_en+0.05)
• Eq (11) Resolution level: 1 - sqrt(activation)
• Eq (12) Securing threshold: S_cert/(S_cert+0.05) * S_int^3
• Eq (13) Selection threshold: fuzzy_equal(S_comp, 1, 15)
• Eqs (14)--(17) Feeling/emotion intensity and fuzzy_low / fuzzy_high helpers.

Relevance to Hyperon

This paper is the canonical mathematics source for the view (MetaMo) not supported for Hyperon AI Algorithms+MetaMo (Motivational Framework) motivational lineage. The 2011 conceptual precursor (OpenPsi: Realizing Doerner's PSI Cognitive Model, AGI-11) describes the architecture but lacks the formal equations. The 2013 paper provides the equations that the current MeTTa port (iCog-Labs-Dev/hyperon-openpsi) attempts to recover.

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Curated Excerpts (cluster-pilot extraction, 2026-04-28)

OpenPsi cluster pilot Source 3 (Papers, 2026-04-28) audited the executable realization of the 2013 paper's mathematics across Classic OpenPsi (Scheme/C++), the iCog-Labs-Dev MeTTa port, and the Hanson dialogue runtime branch. Cross-model triangulation: Claude orchestrator + Codex + Gemini reviewers. The reconciliation file is scripts/archive/openpsi_pilot/source3_papers/findings_reconciled_crossmodel.txt.

Equation-by-equation status against the iCog-Labs-Dev MeTTa port (hyperon-openpsi)

Source 3 verdict: HYBRID / PAPER-LEANING REIMPLEMENTATION, not strict-literal Tradition 6. Equation tally: 8 LITERAL, 2 DIVERGENT, 1 ABSENT, 4 STRUCTURAL.

• Literal (8): Eqs (1) demand satisfaction at demand.metta:158; (2) fuzzy_equal at psi_utils.metta:68; (6) fuzzy_new; (7) competence; (9) fuzzy_near; (10) activation at modulator-updaters.metta:2; (12) securing at modulator-updaters.metta:9; (13) selection at modulator-updaters.metta:16.
• Divergent (2): Eqs (5) certainty and (8) affiliation -- the MeTTa port's denominator structure does not match the paper's parenthesization. The paper's (1+exp(...)) * (n+1) outer-product denominator is rendered in MeTTa as a different grouping at (/ (+ $summation $rand) (+ 1 (* $x (+ 1 $object-num)))).
• Absent (1): Eq (11) resolution_level -- no implementation in modulator-updaters.metta; verified absent via git grep "resolution|sqrt".
• Structural (4): Eqs (14)--(17) -- feeling/emotion intensity helpers are present but evaluated in a different reduction order; matches conceptually but not literal.
• Hardcoded state issue: Several modulator inputs (notably certainty and integrity) are hardcoded to 0.5 in the MeTTa port rather than driven by time-varying perceptions; this is a partial-implementation gap, not a paper divergence.

Tradition placement

The 2013 paper sits in the OpenPsi cluster's mathematical-tradition map as the paper-leaning HYBRID MeTTa line. Two competing implementation traditions are confirmed by the cluster pilot:

• Classic surrogate lineage (mathematical Tradition 2): Upstream opencog/openpsi Scheme + C++. The 819-line slope-based exponential surrogate (slope^(a*x)-1) / (slope^a-1) at opencog/openpsi/dynamics/updater.scm was contributed by Amen Belayneh (commit 48ee8a0bc, 2017-07-24, "Create (opencog openpsi dynamics) guile module"). Classic OpenPsi did not pursue paper-equation faithfulness.
• Paper-leaning HYBRID MeTTa lineage: The iCog-Labs-Dev MeTTa port re-literalized eqs (1)--(2), (6)--(7), (9)--(10), (12)--(13) (commit 01936f1 2026-02-24 by Mahider-n "align activation, securing, resolution, and selection formulas with OpenPsi paper (eq. 10-13)") but did not complete the paper recovery: eq (11) absent, eqs (5)/(8) parenthesization diverges, certainty/integrity hardcoded.

A separate Hanson dialogue/robotics runtime branch (Sophia stack via ros-behavior-scriptingand loving-ai-ghost) consumed Classic OpenPsi as a behavior-loop authority but did not pursue paper-equation faithfulness; Hanson's opencog forkstoppedopencog/openpsi/dynamics/ tracking upstream OpenPsi at 2016-06 master and missed the entire mathematical buildout. This is a runtime/application branch, not a separate mathematical tradition.

Cross-cluster identity notes

The wiki's RawData parent RawData+Publications+Openpsi Zhenhua preserves the verbatim source text under a non-canonical wiki title (the lead author's given name); editorial metadata at the parent disambiguates. The 2011 conceptual precursor at +OpenPsi Cognitive Model (Cai/Goertzel/Geisweiller, AGI-11, LNAI Springer) describes the architecture but lacks the formal equations and is not the source for the iCog-Labs-Dev MeTTa port's mathematical recovery.

For the full per-source extraction archive, see scripts/archive/openpsi_pilot/ in the wiki repository (4 source briefs + 12 findings/reconciliation files). For the related ECAN-attention coupling lifecycle, see +Guiding PLN with Attention Allocation.