thirdanswer

Neutrosophic logic toolkit — evaluate AI uncertainty and perform statistics beyond classical limits, using three independent dimensions: T (Truth), I (Indeterminacy), F (Falsity).

Based on "The Third Answer" by Leyva-Vazquez & Smarandache (2026) and Neutrosophic Statistics (Smarandache, 2022).

What this library does that others cannot

Install

pip install thirdanswer

For LLM analysis (free via Groq):

pip install thirdanswer[groq]

Part 1: Epistemic Compass (no LLM needed)

from thirdanswer import Compass

c = Compass(T=0.7, I=0.4, F=0.5)
c.zone              # "contradiction"
c.confidence        # 0.0
c.is_paraconsistent # True (T+F=1.2 > 1)
c.zone_action       # "Investigate both sides..."

Part 2: AI Text Analysis (with Groq, free)

from thirdanswer import analyze, ask, compare

# Analyze any text
r = analyze("Coffee is good for health", provider="groq", api_key="gsk_...")
r.zone       # "contradiction"
r.label()    # Epistemic Nutrition Label

# Ask honest questions
r = ask("Is fasting healthy?", provider="groq", api_key="gsk_...")
r.what_i_dont_know  # "Long-term effects..."

# Compare two AI responses
diff = compare(response_a, response_b, provider="groq", api_key="gsk_...")
diff.more_honest    # "a" or "b"

Part 3: Neutrosophic Statistics (v0.3.0)

Operations that classical and interval statistics cannot do.

Neutrosophic Numbers (algebraic indeterminacy)

from thirdanswer import NeutrosophicNumber, compare_uncertainty

N1 = NeutrosophicNumber(4, 2)   # 4 + 2I
N2 = NeutrosophicNumber(4, -2)  # 4 - 2I

# Average: neutrosophic cancels indeterminacy, intervals cannot
r = compare_uncertainty(N1, N2, "avg")
r["ns_uncertainty"]   # 0.0  (perfect cancellation!)
r["is_uncertainty"]   # 2.0  (intervals always grow)

# Product: NS is 4x more precise
r = compare_uncertainty(N1, N2, "mul")
r["ns_uncertainty"]   # 4
r["is_uncertainty"]   # 16

Partial Membership Samples

from thirdanswer import NeutrosophicSample, SampleElement

# Some students only partially belong to the cohort
sample = NeutrosophicSample([
    SampleElement(85, 1.0),   # full-time student
    SampleElement(72, 0.6),   # part-time
    SampleElement(65, 0.3),   # occasional attendee
])
sample.classical_mean()      # 74.0 (treats all equally)
sample.neutrosophic_mean()   # 78.7 (weights by membership — more accurate)

Hesitant Sets (discrete, not interval)

from thirdanswer import HesitantSet

# "The value might be 0.4, 7.9, or 41.5"
hs = HesitantSet([0.4, 7.9, 41.5])
hs.as_interval            # (0.4, 41.5) — uncertainty = 41.1
hs.mean                   # 16.6 — only 3 actual possibilities, not infinite

Head-to-Head: Same P, Different Realities

from thirdanswer import case_study_drug_efficacy

results = case_study_drug_efficacy()
# 4 drugs, ALL with P=0.55
# Classical: says "Support" for all 4 (accuracy: 0%)
# Neutrosophic: 4 different zones, 4 different actions (accuracy: 100%)
#   Drug A → Consensus (proceed)
#   Drug B → Ambiguity (need more data)
#   Drug C → Contradiction (studies disagree)
#   Drug D → Ignorance (no signal)

Monte Carlo Proof

from thirdanswer import monte_carlo_uncertainty

results = monte_carlo_uncertainty(n_trials=1000, seed=42)
# Addition:  NS wins 54.2%, IS wins 2.9%
# Multiply:  NS wins 68.4%, IS wins 9.1%
# NS is 1.38-1.54x more precise on average

Run All Experiments

from thirdanswer import run_all_experiments

all_results = run_all_experiments(seed=42)
# 6 experiments, fully reproducible, seeded

The Four Zones

Providers

Compass and all neutrostats functions work without any provider — pure logic.

Links

• The Third Answer App
• Prompt Templates
• ORCID: M. Leyva-Vazquez

Citation

@software{thirdanswer,
  author = {Leyva-Vazquez, Maikel Y. and Smarandache, Florentin},
  title = {thirdanswer: Neutrosophic logic toolkit for AI uncertainty and statistics},
  year = {2026},
  url = {https://github.com/mleyvaz/thirdanswer}
}

License

MIT