The Mechanism · Gated-generation receipt

gen-define-predicate-logic-and-give-one-short-worked-example-3d7b

stable pending witness
2026-05-29 08:12:20 UTC · anthropic/claude-sonnet-4-5

Prompt

Define predicate logic and give one short worked example.
57 chars

Generation

# Predicate Logic **Predicate logic** (also called first-order logic) is an extension of propositional logic that allows us to reason about objects, their properties, and relationships between them. It introduces: - **Predicates**: properties or relations (e.g., P(x) = "x is prime") - **Variables**: placeholders for objects (e.g., x, y, z) - **Quantifiers**: - ∀ (universal): "for all" - ∃ (existential): "there exists" ## Worked Example **Problem**: Translate and prove: "All humans are mortal. Socrates is human. Therefore, Socrates is mortal." **Translation**: - Let H(x) = "x is human" - Let M(x) = "x is mortal" - Let s = Socrates Premises: 1. ∀x (H(x) → M(x)) — "All humans are mortal" 2. H(s) — "Socrates is human" Conclusion: M(s) — "Socrates is mortal" **Proof**: 1. ∀x (H(x) → M(x)) — Premise 2. H(s) → M(s) — Universal instantiation (from 1, substitute s for x) 3. H(s) — Premise 4. M(s) — Modus ponens (from 2 and 3) Therefore, Socrates is mortal. ∎
18 tokens in · 373 tokens out · 7175 ms · $0.0056

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
7186.9 ms
Base LLM
7175.3 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0056

Trail

08:12:20 received prompt_chars=57 verifiers=['scripture_anchors', 'theology_doctrine']
08:12:20 red_gate decision=pass reason=no disqualifying input patterns detected
08:12:27 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=18 tokens_out=373 latency_ms=7175.3 cost_usd=0.0056
08:12:27 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:12:27 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:12:27 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:12:27 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:12:27 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:12:27 signed hash_algo=sha256 hash=sha256:8e3954050f8cb764e3288b27169d2a658b9057570ea5c99dae68c6d2ac41d647

Content hash

sha256:8e3954050f8cb764e3288b27169d2a658b9057570ea5c99dae68c6d2ac41d647

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

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