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Reference — lib_pln.metta

Probabilistic Logic Networks (PLN) — a higher-order probabilistic reasoning framework compatible with the AtomSpace. PLN is the engine to reach for when a problem is best expressed as property-based categorical inference rather than the asymmetric inheritance chains NAL specializes in.

Relations

Atom Meaning
Inheritance Probabilistic "is-a" relation.
Implication Conditional probability — (Implication P Q) ≈ `P(Q
IntSet Intensional set — members share a property.

Truth values share NAL's (stv frequency confidence) format, interpreted probabilistically.

The |~ operator

|~ applies PLN rules. OmegaClaw's current deployment supports a useful subset; the rest are left to NAL or future work.

Rule catalogue — confirmed

Modus Ponens

Primary PLN inference.

Shape: (Implication P Q) and P ⊢ Q.

Truth function:

f = f₁ × f₂
c = f₁ × f₂ × c₁ × c₂

Same shape as NAL deduction — confidence decays linearly.

Abduction (on Inheritance premises)

Shape: supports abduction over Inheritance premises.

Empirical check: (Inheritance bird flyer) + (Inheritance robin flyer) ⊢ (Inheritance robin bird) (stv 0.767 0.422).

Note the output confidence 0.422 — comparable to NAL's abduction ceiling (~0.45). Abduction produces hypotheses worth testing, not actionable conclusions.

Revision

Shape: two beliefs about the same statement.

Truth function: identical to NAL revision.

w = c / (1 - c)
w_total = Σ w_i
c_out = w_total / (w_total + 1)
f_out = weighted average of f_i by w_i

Use revision to merge evidence across PLN conclusions, across NAL conclusions, or across both — the math is the same.

What does NOT work in PLN (current deployment)

Pattern Status
PLN abduction (general case beyond confirmed shapes) Returns empty in practice despite theoretical support.
Backward inference Forward inference only.

If PLN returns empty, reformulate as NAL or try a different premise shape. See recovery guidance in reference-orchestration.md.

Invocation

Through the (metta ...) skill. Variables use $1, $2, …

Modus Ponens example

(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 ...).

Abduction example

(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).

NAL vs. PLN — which to use

Situation Engine
Asymmetric chain A → B → C NAL |-
Observed effect, seeking cause (simple) NAL |- abduction
Merging independent evidence Either (identical formula)
Property-based categorical inference PLN |~
Higher-order structures (Implication over Inheritance) PLN |~
Real-time or temporal reasoning Not served by a stock engine — ONA is the planned future target (see reference-lib-ona.md, experimental, not installed). Current fallback: NAL with external temporal grounding.

When in doubt, try NAL first; PLN shines on Implication over Inheritance chains.

See also