The Mechanism · Gated-generation receipt

gen-define-propositional-logic-and-give-one-short-worked-example-b9d8

stable pending witness
2026-05-29 06:23:51 UTC · anthropic/claude-sonnet-4-5

Prompt

Define propositional logic and give one short worked example.
61 chars

Generation

# Propositional Logic **Propositional logic** is a formal system of reasoning that deals with propositions (statements that are either true or false) and logical connectives that combine them. **Basic connectives:** - ¬ (NOT/negation) - ∧ (AND/conjunction) - ∨ (OR/disjunction) - → (IF-THEN/implication) - ↔ (IF AND ONLY IF/biconditional) ## Worked Example **Premises:** 1. If it is raining, then the ground is wet. (R → W) 2. It is raining. (R) **Conclusion:** Therefore, the ground is wet. (W) **Proof using Modus Ponens:** | Step | Statement | Justification | |------|-----------|---------------| | 1 | R → W | Premise | | 2 | R | Premise | | 3 | W | Modus Ponens (1, 2) | This is valid because modus ponens states: if we have "P → Q" and "P", we can conclude "Q".
19 tokens in · 278 tokens out · 5176 ms · $0.0042

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
5186.1 ms
Base LLM
5175.5 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0042

Trail

06:23:51 received prompt_chars=61 verifiers=['scripture_anchors', 'theology_doctrine']
06:23:51 red_gate decision=pass reason=no disqualifying input patterns detected
06:23:56 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=278 latency_ms=5175.5 cost_usd=0.0042
06:23:56 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:23:56 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:23:56 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:23:56 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:23:56 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:23:56 signed hash_algo=sha256 hash=sha256:aab0a6ec36bce7ca84e69586c579260a51b8ddec7fa3604ff2489c6f4984db57

Content hash

sha256:aab0a6ec36bce7ca84e69586c579260a51b8ddec7fa3604ff2489c6f4984db57

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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