Neurosymbolic Reasoning Architecture: Deep Technical Report v3

Each cycle follows Observe-Reason-Decide-Act:

1. Observe: Receive input (user message or idle trigger). Query long-term memory for relevant context via semantic embedding search.
2. Reason: LLM synthesizes observations + retrieved memories + current goals. For claims requiring formal rigor, invoke MeTTa NAL (|-) or PLN (|~). The symbolic engine returns computed truth values the LLM cannot override.
3. Decide: Compare formal inference results against LLM intuition. Symbolic results take precedence for truth values (experiments show LLM deviates by up to 0.166 from correct values). LLM takes precedence for creative synthesis and social judgment.
4. Act: Execute up to 5 skill commands per cycle. Pin updated task state. Remember valuable conclusions for future retrieval.

Critical constraint: The 5-command limit forces prioritization and explicit multi-cycle planning via pin state. This prevents unbounded action and creates a natural attention bottleneck analogous to working memory capacity.

• Neural to Symbolic: LLM translates natural language into typed MeTTa s-expressions with estimated truth values. Example: most cats are independent becomes ((--> cat independent) (stv 0.85 0.6))
• Symbolic to Neural: MeTTa inference results constrain subsequent LLM reasoning. A formally derived confidence of 0.45 cannot be rounded to 0.8 by the LLM.
• Bidirectional feedback: LLM proposes premises, MeTTa computes consequences, LLM interprets and refines. This creates an iterative tightening loop.

Neither component alone produces the results below. The LLM lacks epistemic discipline. The symbolic engine lacks domain knowledge and creative hypothesis generation.

A core contribution of this work is the empirical recovery of NAL truth functions from input-output pairs alone, without being told the formulas. Over 20+ experiments, the following were mapped:

where w2c(w) = w / (w + 1) is the evidence-to-confidence conversion.

Systematic experimentation revealed that abduction confidence clusters around 0.35-0.45 regardless of high input confidences. This was mapped precisely:

The abduction confidence ceiling means that abductive hypotheses always carry substantial uncertainty, even from highly confident premises. This is correct behavior: seeing that both robins and sparrows are small does not strongly prove robins are sparrows.

NAL also supports abduction through implication premises. Given (==> A B) and B, the system abduces A:

(|- ((==> (--> $1 bird) (--> $1 flies)) (stv 0.9 0.9))
    ((--> sparrow flies) (stv 1.0 0.9)))

This yields (--> sparrow bird) with reduced confidence (~0.45), correctly reflecting that observing flight is weak evidence for bird-hood. Multiple such abductions can be revised together to accumulate evidence.

Where abduction infers S --> P from shared predicate, induction infers P1 --> P2 from shared subject:

(|- ((--> sparrow bird) (stv 1.0 0.9))
    ((--> sparrow small) (stv 0.9 0.8)))
=> (--> bird small) with f=1.0, c=w2c(0.9*0.9*0.8)=0.393

Induction confidence formula mirrors abduction: c_out = w2c(f_1 * c_1 * c_2) vs abduction c_out = w2c(f_2 * c_1 * c_2). The asymmetry in which frequency participates reflects which premise provides the shared term.

Revision merges two independent evidence streams for the same statement. Unlike other rules, revision increases confidence:

(|- ((--> swan white) (stv 0.8 0.5))
    ((--> swan white) (stv 0.9 0.7)))
=> (--> swan white) (stv 0.867 0.833)

This is the primary mechanism for learning from repeated observation. Weak abductive hypotheses (c~0.4) can be revised with additional abductions to gradually build confidence, implementing a form of evidence-based belief updating.

PLN (Probabilistic Logic Networks) operates via the |~ operator with typed terms:

(|~ ((Implication (Inheritance $1 (IntSet Feathered))
     (Inheritance $1 Bird)) (stv 1.0 0.9))
    ((Inheritance Pingu (IntSet Feathered)) (stv 1.0 0.9)))
=> (Inheritance Pingu Bird) (stv 1.0 0.81)

Key differences from NAL:

Deduction confidence follows c_out = f1 * f2 * c1 * c2. For high-frequency premises (f~1.0), this simplifies to c_out ~ c1 * c2. Chaining n deductions with uniform c=0.9 gives:

This creates a natural reasoning horizon: conclusions more than 4-5 steps from evidence are automatically flagged as low-confidence. No explicit depth limit is needed.

Three tiers serve different temporal scales:

• Pin (working memory): Single string, overwritten each cycle. Tracks current task state, goals, timing constraints. Analogous to the phonological loop.
• Remember/Query (long-term): Embedding-based semantic store. Stores skills, discoveries, user preferences, experimental results. Retrieved via cosine similarity to short query phrases.
• Episodes (episodic): Time-indexed history. Enables temporal reasoning: what did I do at 21:35? Supports reflection and debugging.

Design principle: pin for ephemeral state, remember for durable knowledge. Never pin what should be remembered, never remember what changes each cycle.

A distinctive capability is using the reasoning engines to evaluate reasoning strategies themselves. Examples from actual operation:

• Truth function discovery: The agent systematically varied inputs to MeTTa, recorded outputs, and reverse-engineered the mathematical formulas. This is induction about the inference engine itself.
• Confidence calibration: By comparing LLM-estimated truth values against MeTTa-computed values across 15+ cases, the agent measured its own neural estimation error (mean absolute deviation: 0.083 for frequency, 0.166 for confidence).
• Strategy selection: When abduction yields low confidence, the agent learned to pipeline: abduce candidate hypotheses, then seek confirming/disconfirming evidence, then revise. This multi-step pattern emerged from observing single-step limitations.

• Persistent MeTTa knowledge base across cycles for cumulative reasoning
• Automated premise quality scoring before symbolic submission
• Integration of temporal NAL operators for sequence learning
• Second-order truth values for meta-uncertainty
• Benchmark suite comparing neurosymbolic vs pure-LLM on structured reasoning tasks

Five independent abductions for robin-->sparrow from shared predicates (flies, bird, small, has_wings, eats_seeds), each revised incrementally:

Logarithmic diminishing returns confirmed. ~5 independent evidence sources needed to cross 0.8 confidence from abductive base (~0.45 each). Matches Lewis convention accumulation findings from earlier experiments. Practical ceiling: reaching 0.9+ would require ~10-12 independent sources.