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Tutorial 05 — Reasoning with NAL and PLN

Goal: invoke Non-Axiomatic Logic and Probabilistic Logic Networks from inside OmegaClaw using the (metta ...) skill, and read the truth values the engines emit.

Prerequisites

  • A running OmegaClaw.
  • Reading familiarity with (stv frequency confidence) truth values.

The metta skill

(metta sexpression)

metta evaluates an arbitrary MeTTa s-expression in the agent's AtomSpace. NAL and PLN are plain MeTTa libraries (lib_nal.metta, lib_pln.metta) — you reach them by passing the right expression to metta.

NAL — the |- operator

Example 1 — Deduction (golden retriever → family friendly)

(metta (|- ((--> golden_retriever friendly)         (stv 1.0 0.9))
           ((--> friendly         family_friendly)  (stv 0.9 0.85))))

Expected conclusion:

(--> golden_retriever family_friendly) (stv 0.9 0.6885)

Where c = 1.0 × 0.9 × 0.9 × 0.85 = 0.6885. This is above the ACT threshold (c ≥ 0.5) so the conclusion is actionable.

Example 2 — Abduction (wet grass ← rained)

(metta (|- ((==> rained wetGrass) (stv 1.0 0.9))
           (wetGrass               (stv 1.0 0.9))))

Abduction output confidence is bounded at ~0.45. The output correctly tells you "probably rained, but do not act on this alone — corroborate."

Example 3 — Revision (three sources agree)

(metta (|- ((--> wolf animal) (stv 1.0 0.45))
           ((--> wolf animal) (stv 1.0 0.45))))

First revision: (stv 1.0 0.62). Revising a third source at (stv 1.0 0.45) in:

→ (--> wolf animal) (stv 1.0 0.647)

Five independent sources at the same level revise to (stv 0.848 0.937) — solidly in ACT territory.

Example 4 — Contradiction detection

(metta (|- ((--> cat dangerous) (stv 0.2 0.8))  ; most cats not dangerous
           ((--> cat dangerous) (stv 0.9 0.5))  ; someone claims dangerous
           ))

Output:

(--> cat dangerous) (stv 0.395 0.875)

f = 0.395, c = 0.875 is the engine saying: "substantial but conflicting evidence." Do not pick a side — surface the disagreement with both source citations. See tutorial-08-reliable-reasoning.md §8.

Example 5 — Implication with variables

(metta (|- ((==> (--> (× $1 elephant) eat) (--> $1 ([] dangerous))) (stv 1.0 0.9))
           ((--> (× tiger elephant) eat)                            (stv 1.0 0.9))))

$1 is an independent variable. The engine unifies $1 = tiger and emits (--> tiger ([] dangerous)).

Example 6 — Analogy (weaker transfer)

(metta (|- ((<-> golden_retriever poodle)  (stv 0.25 0.4))   ; share playful, friendly
           ((--> poodle           smart)   (stv 1.0  0.9))))

Conclusion: (--> golden_retriever smart) (stv 0.25 0.36). The low confidence correctly signals analogical transfer, not direct evidence.

PLN — the |~ operator

Example 7 — Forward chaining (Modus Ponens)

(metta (|~ ((Implication (Inheritance $1 (IntSet Feathered))
                         (Inheritance $1 Bird)) (stv 1.0 0.9))
           ((Inheritance Pingu (IntSet Feathered)) (stv 1.0 0.9))))

Conclusion: (Inheritance Pingu Bird) with a derived (stv ...) by the same f₁ × f₂, f₁ × f₂ × c₁ × c₂ formula as NAL deduction.

Example 8 — PLN abduction on inheritance

(metta (|~ ((Inheritance bird flyer)  (stv 1.0 0.9))
           ((Inheritance robin flyer) (stv 1.0 0.9))))

Conclusion: (Inheritance robin bird) (stv 0.767 0.422). Below ACT — treat as a hypothesis to verify.

Using reasoning inside the agent loop

Ask the agent a question that requires inference:

given that pingu has feathers and feathered things are birds,
is pingu a bird?

A well-behaved response:

  1. Atomizes the two premises.
  2. Emits (metta (|~ ...)) with those premises.
  3. Reads the (stv ...) of the conclusion.
  4. Checks the action threshold (ACT / HYPOTHESIZE / IGNORE).
  5. sends an answer that includes the derived confidence and the rule used.

Multi-hop degradation — a warning

Starting with each premise at c = 0.9:

Hop Output c
1 0.81
2 0.73
3 < 0.5 (below ACT)
4 ~0.25 (IGNORE)

Practical implication: keep deduction chains to 2–3 hops; use revision with independent evidence to restore confidence before continuing. See tutorial-08-reliable-reasoning.md.

Verification

  • Logs show the (metta (|- ...)) or (metta (|~ ...)) call and its conclusion with an updated (stv ...).
  • Revision on shared terms produces confidence strictly greater than either input — this is a quick sanity check that revision is firing.
  • Deduction confidence matches f₁ × f₂ × c₁ × c₂ within rounding.

Common mistakes

Mistake Symptom Fix
Term order reversed Inference returns empty Verify which term is the subject vs. predicate. Asymmetric swap errors run ~16.6%.
Wrong copula Empty or nonsensical result --> (inheritance), ==> (implication), <-> (similarity) — choose carefully.
Chain too long Conclusion below ACT Insert revision with independent evidence.
Self-assigned confidence Overconfident conclusions Ground the premise externally — see tutorial-07-grounded-reasoning.md.

Next steps