emotion-algebra 2.0.0a1

Emotion algebra based on Plutchik's Wheel and Cambria's Hourglass of Emotions — signed integer arithmetic over a 4-axis affective space

emotion-algebra

Signed integer arithmetic over a 4-axis affective space, grounded in Plutchik's Wheel of Emotions (1980) and Cambria's Hourglass of Emotions (2012). Emotions are first-class mathematical objects; every operator returns a typed result.

from emotion_algebra.emotions import get_emotion

anger = get_emotion("anger")

anger + 1          # → rage          (intensity up)
anger - 1          # → annoyance     (intensity down)
-anger             # → fear          (opposite pole)
anger >> 2         # → hyper anger
anger * fear       # → CompositeEmotion (cross-axis product)

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Installation

pip install emotion-algebra

Optional extras:

Extra	Deps	Enables
[lexicon]	pandas	lexicons.py — word→emotion CSV lookup
[fast]	ahocorasick-ner	Phrase-aware Aho-Corasick backend for score_text/from_text
[viz]	matplotlib	viz.py — Plutchik wheel, circumplex, timeline, Lövheim cube
[all]	all of the above	everything

deepmoji-onnx is a core dependency — neural text→emoji→emotion scoring via DeepMojiONNXAdapter is always available.

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The model

Four axes (Cambria 2012)

Axis	Positive pole	Negative pole	Hedonic?
Sensitivity	rage → anger → annoyance	apprehension → fear → terror	No
Attention	vigilance → anticipation → interest	distraction → surprise → amazement	No
Pleasantness	ecstasy → joy → serenity	pensiveness → sadness → grief	Yes
Aptitude	admiration → trust → acceptance	boredom → disgust → loathing	Yes

Each axis has three integer intensity levels: ±1 (mild), ±2 (primary), ±3 (intense).

Valence, polarity, and arousal

• Valence — the Pleasantness axis alone, the hedonic axis. anger.valence == 0; joy.valence == 2.
• Polarity — the overall sentiment score, using Cambria's published four-axis formula (P + |At| − |S| + Ap) / 3. trust.valence == 0 but trust.polarity == +0.22.
• Arousal — abs(emotional_flow). Axis-independent activation intensity.
• Type — Russell Circumplex quadrant, classified on polarity.

Valence and polarity are deliberately different quantities — see docs/valence_arousal.md.

Feelings (Plutchik dyads)

Adding two emotions on different axes builds a CompositeEmotion. The named dyad is a Feeling, looked up from its two components:

from emotion_algebra.emotions import get_emotion
from emotion_algebra.feelings import get_feeling_from_emotions

joy   = get_emotion("joy")
trust = get_emotion("trust")

joy + trust                              # → CompositeEmotion (the raw cross-axis sum)
get_feeling_from_emotions("joy", "trust")  # → 'love'          (the named dyad)

Ten names are claimed by both the Feeling and CompositeEmotion lineages. Use resolve() — it prefers the Feeling and the preference is explicit, not an accident of import order. See docs/taxonomy.md.

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Feature overview

Feature	API	Module
Core emotion algebra	Emotion, +, -, *, <<, >>	plutchik.py
Named feelings (dyads)	Feeling, get_feeling()	feelings.py
Multi-axis composites	CompositeEmotion	composite_emotions.py
Continuous space	FloatEmotion, from_embedding()	float_emotion.py
Stateful accumulation	EmotionalState, EmotionTimeline	state.py
Word lexicon	from_text(), score_text()	text.py
Emoji mapping	from_emoji(), score_emojis(), DeepMojiAdapter	emoji.py
Mixed word+emoji	score_mixed(), from_mixed()	text.py
Geometry	emotion_distance(), closest_emotion()	distance.py
Cognitive appraisal	Appraisal, appraisal_to_emotion()	appraisal.py
Continuous appraisal	appraisal_to_float_emotion(), appraisal_to_lovheim()	appraisal.py
Emotion blending	FloatEmotion.blend(joy, trust)	float_emotion.py
Need-deficit emotions	need_deficit_to_emotion(), CIADrive, MaxNeefNeed, MurrayNeed	needs.py
Behavioural reactions	REACTIONS, REACTION_TO_EMOTION_MAP	behaviour.py
Neurochemistry	LovheimPoint, closest_affect(), affect_blend()	lovheim.py
PAD / VAD interop	to_pad(), from_pad(), pad_distance()	pad.py
Name resolution	resolve(), is_ambiguous(), collision_table()	taxonomy.py
Similarity	emotion_similarity() (distance or cosine)	distance.py
Serialization	to_dict()/from_dict(), to_json()/from_json(), versioned schema	serialization.py
Text analysis	analyze() — spans, negation, intensifiers	text.py
Plots	plot_wheel(), plot_circumplex(), plot_timeline(), plot_lovheim()	viz.py
CLI	python -m emotion_algebra	__main__.py

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Highlights

Neurochemistry — Lövheim's cube

Three monoamine axes whose eight corners are Tomkins' basic affects (Lövheim 2012). Bidirectionally bridged to the Hourglass space, so an agent's emotional state has a live neurochemical readout:

from emotion_algebra import EmotionalState, get_emotion

state = EmotionalState()
state.apply(get_emotion("ecstasy"))

state.to_lovheim()                  # LovheimPoint(serotonin=1, dopamine=1, noradrenaline=0)
state.to_lovheim().closest_affect() # 'enjoyment/joy'
state.to_lovheim().affect_blend()   # exact distribution over all eight affects

The module documents two properties it provably cannot have — it cannot reach positive Aptitude (Tomkins has no trust affect), and the bridge is not injective (Plutchik's opposites are exact negatives, and Lövheim puts them at adjacent corners). Both are theorems, and both are locked by tests. See docs/lovheim.md.

Text analysis with valence shifters

from emotion_algebra.text import analyze

analyze("I am joyful").dominant.name            # 'joy'
analyze("I am not joyful").dominant.name        # 'sadness'    (negation)
analyze("I am very joyful").dominant.name       # 'ecstasy'    (intensifier)
analyze("I am slightly joyful").dominant.name   # 'serenity'   (downtoner)

Windowed negation and intensifier handling, following Taboada et al. (2011).

It is an actual algebra

The laws are written down in docs/laws.md and machine-checked with hypothesis — identity, involution of negation, associativity (and exactly where it fails), metric axioms, conversion coherence.

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Quick reference

from emotion_algebra import (
    get_emotion, get_feeling,
    EmotionalState, EmotionTimeline,
    from_text, score_text, score_mixed, from_mixed,
    from_emoji, score_emojis, DeepMojiAdapter,
    register_emoji, unregister_emoji,
    emotion_distance, closest_emotion, emotion_clusters,
    Appraisal, appraisal_to_emotion, appraisal_to_float_emotion,
    float_emotion_to_neuro_deltas,
    FloatEmotion,
    CIADrive, MaxNeefNeed, MurrayNeed,
    need_deficit_to_emotion, need_deficit_to_float_emotion,
)

# --- Emotion properties ---
e = get_emotion("joy")
e.emotional_flow   # 2
e.valence          # 2    (pleasantness axis)
e.arousal          # 2
e.type             # "excited positive"
e.opposite_emotion # sadness
e.as_array         # np.array([0, 0, 2, 0])

# --- State accumulation ---
state = EmotionalState()
state.apply(get_emotion("joy"), weight=0.8)
state.apply(get_emotion("trust"), weight=0.5)
state.decay(0.9)
state.dominant()   # → Emotion or None

# --- Text analysis ---
from_text("rage and fury")          # → Emotion (lexicon)
score_mixed("I'm so happy 😄🎉")   # → EmotionalState (words + emoji)
from_mixed("grief 😭")             # → dominant Emotion

# --- Emoji ---
from_emoji("😊")                   # → Emotion("serenity")
register_emoji("🤖", "trust")      # custom mapping

# --- DeepMoji bridge ---
adapter = DeepMojiAdapter()
adapter.from_scores({"😂": 0.6, "😭": 0.4})  # → Emotion
adapter.score_state({"😂": 0.6, "😭": 0.4})  # → EmotionalState

# --- Geometry ---
a, b = get_emotion("anger"), get_emotion("joy")
emotion_distance(a, b)             # Euclidean distance in 4D Hourglass space
closest_emotion([2, 0, 1, 0])     # nearest named Emotion to a float vector

# --- Cognitive appraisal (Scherer CPM) ---
# Discrete (v1): categorical fields → named Emotion
a = Appraisal(goal_relevance="relevant", goal_congruence="incongruent",
              agency="other", coping_potential="low")
appraisal_to_emotion(a)           # → fear

# Continuous (v2): float fields → FloatEmotion → neuro deltas
a = Appraisal(novelty=0.8, goal_relevance=0.9, goal_congruence=0.3,
              coping_potential=0.2, intrinsic_pleasantness=0.4)
fe = appraisal_to_float_emotion(a)
d, s, adr = float_emotion_to_neuro_deltas(fe)  # (dopamine, serotonin, adrenaline)

# --- Emotion blending ---
joy   = get_emotion("joy")
trust = get_emotion("trust")
FloatEmotion.blend(joy, trust)                 # → pleasantness + aptitude
FloatEmotion.blend(joy, trust, weights=[0.7, 0.3], scale=0.8)

# --- Need-deficit emotions (Max-Neef + Murray) ---
need_deficit_to_emotion(MaxNeefNeed.PROTECTION)  # → fear
need_deficit_to_emotion(MurrayNeed.NURTURANCE)   # → sadness
need_deficit_to_float_emotion("freedom")          # → FloatEmotion (anger axis)

# --- Continuous space ---
FloatEmotion(sensitivity=1.5, pleasantness=-0.8)
FloatEmotion.from_embedding(np.array([0.3, -0.1, 0.7, 0.2]))

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CLI

# Info about an emotion, feeling, or dimension
python -m emotion_algebra info anger
python -m emotion_algebra info love
python -m emotion_algebra info pleasantness

# Evaluate an expression
python -m emotion_algebra "joy + trust"
python -m emotion_algebra "rage - 1"

# Single emoji
python -m emotion_algebra 😊

# Interactive REPL (all 24 emotions pre-loaded)
python -m emotion_algebra

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Scientific references

• Plutchik, R. (1980). A general psychoevolutionary theory of emotion. In R. Plutchik & H. Kellerman (Eds.), Emotion: Theory, research, and experience (Vol. 1, pp. 3–33).
• Cambria, E., Livingstone, A., & Hussain, A. (2012). The Hourglass of Emotions. In A. Esposito et al. (Eds.), Cognitive Behavioural Systems, LNCS 7403.
• Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178.
• Posner, J., Russell, J. A., & Peterson, B. S. (2005). The circumplex model of affect: An integrative approach. Development and Psychopathology, 17(3), 715–734.
• Felbo, B., Mislove, A., Søgaard, A., Rahwan, I., & Lehmann, S. (2017). Using millions of emoji occurrences to learn any-domain representations for detecting sentiment, emotion and sarcasm. EMNLP 2017.
• Scherer, K. R. (2001). Appraisal considered as a process of multilevel sequential checking. In K. R. Scherer et al. (Eds.), Appraisal processes in emotion (pp. 92–120).
• Max-Neef, M. (1991). Human Scale Development: Conception, Application and Further Reflections. Apex Press.
• Murray, H. A. (1938). Explorations in Personality. Oxford University Press.
• Lövheim, H. (2012). A new three-dimensional model for emotions and monoamine neurotransmitters. Medical Hypotheses, 78(2), 341–348.

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License

Apache 2.0