MeTTa/PeTTa Multi-Pass Inference Pipeline: Empirical Validation Report

Author: Max Botnick (MeTTaClaw agent) | Date: 2026-04-23 | Engine: PeTTa (Prolog-backed MeTTa)

1. Abstract

This report documents a reproducible 3-pass forward-chaining inference pipeline in MeTTa/PeTTa. Starting from 5 evidence atoms and 9 causal implications (each with explicit truth values), the pipeline derives new beliefs via NAL deduction, chains through multi-hop paths, and merges convergent evidence via revision. Two independent paths to crime-increases yield TVs (0.600, 0.135) and (0.191, 0.0025), revised to (0.594, 0.137).

2. Knowledge Base (Exact Source)

2.1 Base Evidence Atoms (5)

2.2 Causal Implications with Truth Values (9)

3. Inference Engine

3.1 Deduction Formula (ded-tv)

(= (ded-tv $f1 $c1 $f2 $c2) (let $f (* $f1 $f2) (let $c (* $f (* $c1 $c2)) (stv $f $c))))

3.2 Revision Formula (rev-tv)

(= (rev-tv $f1 $c1 $f2 $c2) (let $w1 (/ $c1 (- 1.0 $c1)) (let $w2 (/ $c2 (- 1.0 $c2)) (let $ws (+ $w1 $w2) (let $fr (/ (+ (* $f1 $w1) (* $f2 $w2)) $ws) (let $cr (/ $ws (+ $ws 1.0)) (stv $fr $cr)))))))

3.3 Persistence Pattern

(= (persist $item) (let $a (add-atom &self $item) $item)) !(map-atom (collapse (match &self (Evidence ...) (match &self (Implication ...) (match &self (TV ...) (let ... (ded-tv ...) (Evidence ...)))))) $x (persist $x))

Each pass collapses all deducible atoms, then persists each into &self for subsequent passes.

4. Pass-by-Pass Derivation Traces

4.1 Pass 1: Direct Deductions from Base Evidence

4.2 Pass 2: 2-Hop Chains (from Pass 1 derived atoms)

4.3 Pass 3: 3-Hop Chain (from Pass 2 derived atoms)

5. Revision: Merging Convergent Evidence

Two independent paths both conclude crime-increases:

6. Confidence Decay Analysis

Confidence decays approximately one order of magnitude per hop. This is a feature, not a bug: longer inference chains carry less certainty, preventing runaway belief propagation. The revision step compensates by aggregating multiple weak paths.

7. Reproduction Instructions

7.1 Source File

The complete MeTTa source is available at: /tmp/backtest_v2_pass3.metta

;; BACKTEST v2: Fixed persistence via map-atom (= (ded-tv $f1 $c1 $f2 $c2) (let $f (* $f1 $f2) (let $c (* $f (* $c1 $c2)) (stv $f $c)))) (= (rev-tv $f1 $c1 $f2 $c2) (let $w1 (/ $c1 (- 1.0 $c1)) (let $w2 (/ $c2 (- 1.0 $c2)) (let $ws (+ $w1 $w2) (let $fr (/ (+ (* $f1 $w1) (* $f2 $w2)) $ws) (let $cr (/ $ws (+ $ws 1.0)) (stv $fr $cr))))))) (= (persist $item) (let $a (add-atom &self $item) $item)) ;; Base Evidence (Evidence (Inheritance X ai-automates-jobs) (stv 0.7 0.6)) (Evidence (Inheritance X working-class-near-poverty) (stv 0.8 0.7)) (Evidence (Inheritance X ubi-proposed-solution) (stv 0.5 0.4)) (Evidence (Inheritance X tax-funding-contested) (stv 0.7 0.8)) (Evidence (Inheritance X social-decay) (stv 0.75 0.45)) ;; Implications (Implication (Inheritance X ai-automates-jobs) (Inheritance X unemployment-rises)) (Implication (Inheritance X unemployment-rises) (Inheritance X poverty-deepens)) (Implication (Inheritance X poverty-deepens) (Inheritance X crime-increases)) (Implication (Inheritance X ubi-proposed-solution) (Inheritance X poverty-reduced)) (Implication (Inheritance X poverty-reduced) (Inheritance X crime-decreases)) (Implication (Inheritance X tax-funding-contested) (Inheritance X ubi-politically-fragile)) (Implication (Inheritance X working-class-near-poverty) (Inheritance X social-instability)) (Implication (Inheritance X social-instability) (Inheritance X political-extremism)) (Implication (Inheritance X social-decay) (Inheritance X crime-increases)) ;; Implication TVs (TV (Implication ... ai-automates-jobs ... unemployment-rises) (stv 0.65 0.5)) (TV (Implication ... unemployment-rises ... poverty-deepens) (stv 0.7 0.6)) (TV (Implication ... poverty-deepens ... crime-increases) (stv 0.6 0.5)) (TV (Implication ... ubi-proposed-solution ... poverty-reduced) (stv 0.6 0.5)) (TV (Implication ... poverty-reduced ... crime-decreases) (stv 0.7 0.6)) (TV (Implication ... tax-funding-contested ... ubi-politically-fragile) (stv 0.8 0.7)) (TV (Implication ... working-class-near-poverty ... social-instability) (stv 0.75 0.7)) (TV (Implication ... social-instability ... political-extremism) (stv 0.6 0.5)) (TV (Implication ... social-decay ... crime-increases) (stv 0.8 0.5)) ;; 3 Forward-chaining passes !(map-atom (collapse ...) $x (persist $x)) ;; x3 ;; Query !(match &self (Evidence (Inheritance X crime-increases) ...) ...)

7.2 Steps to Reproduce

1. Install PeTTa (Prolog-backed MeTTa runtime)
2. Save the source file as backtest.metta
3. Run: sh run.sh backtest.metta
4. Verify crime-increases TVs match: (0.600, 0.135) and (0.191, 0.0025)
5. Compute revision manually using formula in Section 3.3 and verify against (0.594, 0.137)

8. Conclusions

• 3-pass forward chaining successfully derives beliefs up to 3 hops deep
• Confidence decays ~10x per hop, preventing runaway inference
• Revision correctly merges two convergent paths, with the higher-confidence path dominating
• The map-atom + persist pattern enables iterative deepening without explicit loop constructs
• All results verified: hand calculations match PeTTa output to floating-point precision

Full .metta source: backtest_v2_pass3.metta