gaia

Gaia Lang

Gaia is a formal language for scientific reasoning. It helps you uncover and organize the logical relationships between scientific propositions — deduction, abduction, induction, contradiction — and then computes the probability of each proposition being true. Following the Jaynesian program — built on Cox's theorem that consistent reasoning is uniquely isomorphic to probability theory — these probabilities are objective: once the reasoning structure is defined, they are mathematically determined.

Quick Example

Galileo's thought experiment: tie a heavy stone to a light stone. Does the composite fall faster or slower?

graph TD
    obs_daily["📋 Daily observation (0.90 → 1.00 📈)"]:::premise
    aristotle["🏛️ Aristotle: heavier = faster (0.90 → 0.07 📉)"]:::premise
    air_resistance["🌬️ Air resistance (0.50 → 0.94 📈)"]:::derived
    composite_slower["🪨🪶 < 🪨 Composite slower (0.60 → 0.40 📉)"]:::derived
    composite_faster["🪨🪶 > 🪨 Composite faster (0.60 → 0.40 📉)"]:::derived
    paradox["⚔️ paradox (0.98)"]:::derived
    vacuum_law["💡 Vacuum law (0.30 → 0.96 📈)"]:::derived
    strat_0(["🔍 abduction"])
    obs_daily --> strat_0
    aristotle --> strat_0
    strat_0 --> air_resistance
    strat_1(["🧠 deduction"])
    aristotle --> strat_1
    strat_1 --> composite_slower
    strat_2(["🧠 deduction"])
    aristotle --> strat_2
    strat_2 --> composite_faster
    strat_3(["🧠 deduction"])
    air_resistance --> strat_3
    strat_3 --> vacuum_law
    oper_0{{"⊗ contradiction"}}:::contra
    composite_slower --- oper_0
    composite_faster --- oper_0
    oper_0 --- paradox

    classDef setting fill:#f0f0f0,stroke:#999,color:#333
    classDef premise fill:#ddeeff,stroke:#4488bb,color:#333
    classDef derived fill:#ddffdd,stroke:#44bb44,color:#333
    classDef contra fill:#ffebee,stroke:#c62828,color:#333

The contradiction and abduction are independent subgraphs, yet belief propagation automatically combines both lines of evidence: the contradiction refutes Aristotle (0.90 → 0.07) while the abduction elevates air resistance (0.50 → 0.94), and together they lift the vacuum law from a speculative 0.30 to a near-certain 0.96 — no new experimental data needed, just the structure of the reasoning itself.

The code that produces this:

from gaia.lang import claim, contradiction, deduction, abduction

# 📋 The observation everyone agrees on
obs_daily = claim("Heavy objects fall faster than light ones in air.")

# 🏛️ Two competing explanations
aristotle = claim("🏛️ Speed is proportional to weight — heavier = faster.")
air_resistance = claim("🌬️ The speed difference is caused by air resistance, not weight.")

# 🔍 Abduction: which explanation better accounts for the observation?
abduction(observation=obs_daily, hypothesis=air_resistance, alternative=aristotle,
    reason="Both explain why heavy objects fall faster in air.")

# 🤔 Meanwhile, Aristotle's doctrine implies contradictory predictions
composite_slower = claim("🪨🪶 The composite falls SLOWER than the heavy stone alone.")
composite_faster = claim("🪨🪶 The composite falls FASTER than either stone alone.")
deduction(premises=[aristotle], conclusion=composite_slower,
    reason="If heavier = faster, the light stone drags the heavy one back.")
deduction(premises=[aristotle], conclusion=composite_faster,
    reason="If heavier = faster, the heavier composite must fall faster.")

# ⚔️ Same premise, opposite conclusions — that's a contradiction!
paradox = contradiction(composite_slower, composite_faster,
    reason="Aristotle's own logic predicts both faster AND slower")

# 💡 Remove the air, remove the difference
vacuum_law = claim("💡 In vacuum, all bodies fall at the same rate.")
deduction(premises=[air_resistance], conclusion=vacuum_law,
    reason="If air resistance is the sole cause, removing it means all fall equally.")

How it Works

Python DSL  →  gaia compile  →  Gaia IR (factor graph)  →  gaia infer  →  beliefs

1. Declare propositions and their logical relationships using the Python DSL
2. Compile to Gaia IR — a canonical intermediate representation encoding the reasoning structure as a factor graph
3. Infer — belief propagation computes the posterior probability of every proposition, automatically selecting the best algorithm (exact junction tree for small graphs, loopy BP for larger ones)