STEP: 1533 / Test: 41/41 PASS / Lean 4: 9 theorem zero sorry / Type: STEP 1505 言語 3rd tool (47 defer 20 番目、 姉妹 tool 23)
★★★ SELF⟲ 7/8 領域 tool 完備 到達 — Lawvere / Lyapunov / Evolution / Nash / Halting / Metacognition / Liar (本 tool)。 残 = 物理 1 領域。
❶ Self-referential statement graph → truth-value fixpoint analysis → SELF⟲ verdict。 Symbolic reference graph 入力 (自然言語 parsing 未 embed)。
❂ 7 case 決定表: invalid → NEITHER / self-loop negation → SELF (liar_paradox) / self-loop no-negation → SELF (truth_teller_fixpoint) / n-cycle odd negation → SELF (n_step_liar) / n-cycle even negation → SELF (n_step_fixpoint) / well-founded → TRUE。
❸ 意味論的 SELF⟲ 三姉妹完成: STEP 1524 halting (計算) + STEP 1529 metacognition (認知) + STEP 1533 liar (言語)。
| Condition | Verdict | Reason |
|---|---|---|
| invalid input (empty / target 不在) | NEITHER | invalid_input |
| self-loop, claimedValue=false | SELF ★ | liar_paradox |
| self-loop, claimedValue=true | SELF ★ | truth_teller_fixpoint |
| n-cycle (>1), 奇数回 negation | SELF ★ | n_step_liar |
| n-cycle (>1), 偶数回 negation | SELF ★ | n_step_fixpoint |
| well-founded (no cycle) | TRUE | well_founded |
// Classic Liar
liarParadoxVerdict({
statements: [{ id: 'A', claimsAbout: 'A', claimedTruthValue: 'false' }],
});
// { verdict: 'SELF', reason: 'liar_paradox', cycleLength: 1, negationCount: 1 }
// Truth Teller
liarParadoxVerdict({
statements: [{ id: 'A', claimsAbout: 'A', claimedTruthValue: 'true' }],
});
// { verdict: 'SELF', reason: 'truth_teller_fixpoint' }
// 2-cycle Liar
liarParadoxVerdict({
statements: [
{ id: 'A', claimsAbout: 'B', claimedTruthValue: 'true' },
{ id: 'B', claimsAbout: 'A', claimedTruthValue: 'false' },
],
});
// { verdict: 'SELF', reason: 'n_step_liar', cycleLength: 2, negationCount: 1 }
// Well-founded (external reference)
liarParadoxVerdict({
statements: [{ id: 'A', claimsAbout: 'FACT', claimedTruthValue: 'true' }],
});
// { verdict: 'TRUE', reason: 'well_founded', isWellFounded: true }
liar_invalid_target_gives_neither : invalid target → NEITHER liar_well_founded_gives_true : no cycle → TRUE liar_self_loop_negation_gives_self : self-loop + negation → SELF liar_self_loop_truth_teller_gives_self : self-loop + no negation → SELF liar_any_cycle_gives_self : any cycle → SELF (general) liar_two_cycle_gives_self : 2-cycle → SELF liar_verdict_deterministic : same input → same output liar_odd_parity_gives_self : cycle + odd negations → SELF liar_even_parity_gives_self : cycle + even negations → SELF
| # | Domain | Tool | STEP | SELF⟲ 意味 |
|---|---|---|---|---|
| 1 | 圏論 | Lawvere fp | — | 不動点 圏論的 unique existence |
| 2 | 制御理論 | lyapunov | 1509 | V(t) all equal non-zero → fixpoint |
| 3 | 生物学 | evolution | 1514 | Population stationary → 自己複製 fixpoint |
| 4 | 経済学 | nash | 1520 | Best response 相互不動点 |
| 5 | 情報科学 | halting | 1524 | Execution fixpoint / cycle 検出 |
| 6 | 認知科学 | metacognition | 1529 | 思考の思考 自己参照 depth |
| 7 | 言語学 | liar (本) | 1533 | 真偽値 fixpoint / paradox 循環 |
| 8 | 物理 | (未実装) | — | 次 STEP candidate |
❶ 自然言語 parsing 未 embed — statement は既に符号化された reference graph 前提 (id/claimsAbout/claimedTruthValue の 3 field 手入力)。
❂ Kripke fixed-point theory 完全実装ではない — 基本 cycle detection と parity check のみ。
❸ Tarski 階層 truth predicate (T-schema) 未 embed — 簡易 self-reference detection のみ。
❹ Yablo paradox 変種 (無限降下 chain) は well-founded として扱う (chain 終端 external で TRUE、 有限 sample で cycle 検出しない)。
❺ 累計 defer 29 → 28 (STEP 1533 で 1 tool 追加)。