Catelingo: Constraint-Based Semantic Validity Verification

1. Overview

Catelingo treats semantic validity as a structural property: a sentence is valid iff the semantic constraints induced by the sentence are satisfiable. :contentReference[oaicite:4]{index=4}

Design goal: reject only when the induced constraints are jointly impossible (UNSAT), preserve ambiguity when at least one interpretation remains feasible (SAT), and avoid forced guesses (UNKNOWN). :contentReference[oaicite:5]{index=5}

2. How it works

Pipeline (conceptual)

LLM output → parse/dependencies → sense candidates (ambiguous) →
instantiate constraints (type/range/temporal/invariants) →
propagate constraints on dependency edges → verdict (SAT/UNSAT/UNKNOWN)

Key point: Catelingo does not “pick the most likely meaning”. It keeps all compatible senses and rejects only if all paths die. :contentReference[oaicite:6]{index=6}

Decision semantics

SAT: at least one consistent interpretation remains → ACCEPT
UNSAT: all candidates eliminated by constraints → REJECT
UNKNOWN: underspecified variables prevent a definitive SAT/UNSAT decision → defer / ask for clarification

This is intentionally orthogonal to truth, likelihood, or factual correctness. :contentReference[oaicite:7]{index=7}

3. What Catelingo checks

Constraint classes (typical)

Temporal: ordering relations (e.g., “commemorate” implies construction time ≥ event time)
Numerical: admissible ranges (probability in [0,1], percent in [0,100], unit consistency)
Semantic types: type compatibility and selectional restrictions
Basic physical/physiological invariants: abstract constraints (not encyclopedic facts)

Many hallucinations fall into these “semantic no-go” categories even without reasoning chains. :contentReference[oaicite:8]{index=8}

Meaning as feasible region

Let a sentence induce constraints $C=\{c_1,\dots,c_n\}$. Semantic validity is:

$$\text{Valid}(S)\;\Longleftrightarrow\;\text{SAT}(C)$$ $$\text{Invalid}(S)\;\Longleftrightarrow\;\text{UNSAT}(C)$$

Ambiguity is acceptable: Catelingo requires non-emptiness of the feasible region, not a unique interpretation. :contentReference[oaicite:9]{index=9}

4. Profiles (domain adaptation)

Semantic validity is domain-relative. Catelingo makes this explicit via constraint profiles: switch profiles to change admissibility criteria (e.g., strict finance vs generous poetry) without retraining any model. :contentReference[oaicite:10]{index=10}

Profile = senses + constraints + optional degeneration (metaphor) rules
Adaptation = swap profiles at runtime

5. Complexity intuition

Naive all-pairs semantic checking is quadratic in tokens. Catelingo propagates constraints along dependency edges (typically linear in sentence length), yielding practical near-linear behavior with bounded sense candidates per token. :contentReference[oaicite:11]{index=11}

Naive: $O(n^2 \cdot d^2)$ → Dependency-local: $O(n \cdot d^2)$

6. Relation to System-2 FW / Eidoku

System-2 FW: architectural separation of generation / verification / acceptance
Eidoku: structural feasibility checking for reasoning/output structure
Catelingo: semantic constraint satisfiability (no-go detection) even without reasoning chains

The point is composability: structural verification and semantic constraint verification target orthogonal failure modes. :contentReference[oaicite:12]{index=12}