Formal Specification

正式规范

Multimodal Logic Integration

多模态逻辑集成

Five modal logics via fusion with bridge principles:

JL: Justification Logic - evidence-backed claims
IEL: Inferential Erotetic Logic - question handling
TEL: Temporal Epistemic Logic - phase sequencing
SDL: Standard Deontic Logic - obligations/permissions
DEL: Dynamic Epistemic Logic - action modalities

通过融合桥接原则实现五种模态逻辑：

JL: 辩护逻辑 - 基于证据的主张
IEL: 推理疑问逻辑 - 问题处理
TEL: 时序认知逻辑 - 阶段排序
SDL: 标准道义逻辑 - 义务/权限
DEL: 动态认知逻辑 - 行动模态

Justification Logic (JL)

辩护逻辑（JL）

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Justification terms

辩护术语

[h]:context(task_n) # Handoff h justifies task context [v]:verified(phase_n) # Verification v justifies completion [p]:plan(tasks) # Plan p justifies task list

[h]:context(task_n) # 交接h为任务上下文提供辩护 [v]:verified(phase_n) # 验证v为阶段完成提供辩护 [p]:plan(tasks) # 计划p为任务列表提供辩护

Evidence production

证据生成

[read(f)]exists e. [e]:content(f) [verify(c)]exists v. [v]:pass(c) | [v]:fail(c)

Handoff chain: evidence propagates

交接链：证据传播

[h_n]:complete(task_n) -> [h_{n+1}]:context(task_{n+1}) proceed(task) <-> exists h. [h]:validated

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[h_n]:complete(task_n) -> [h_{n+1}]:context(task_{n+1}) proceed(task) <-> exists h. [h]:validated

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Inferential Erotetic Logic (IEL)

推理疑问逻辑（IEL）

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Mode and blocker questions

模式与阻塞问题

?{direct, orchestration} # Mode selection ?{continue, retry, ask_user} # Blocker resolution mismatch(plan, reality) -> ?{how_proceed} no_validation -> ?{run_validation_first}

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?{direct, orchestration} # 模式选择 ?{continue, retry, ask_user} # 阻塞解决 mismatch(plan, reality) -> ?{how_proceed} no_validation -> ?{run_validation_first}

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Temporal Epistemic Logic (TEL)

时序认知逻辑（TEL）

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File reading constraints

文件读取约束

[](mentioned(f) -> <>read_fully(f)) # Eventually read [](mentioned(f) -> not spawn U read_fully(f)) # No spawn until read [](partial_read(f) -> false) # Partial reads forbidden

[](mentioned(f) -> <>read_fully(f)) # 最终需完整读取 [](mentioned(f) -> not spawn U read_fully(f)) # 读取完成前不启动进程 [](partial_read(f) -> false) # 禁止部分读取

Phase sequencing

阶段排序

[](phase(n) -> P(phase(n-1) & verified(n-1))) # Verified before next [](automated_pass -> <>manual_verify) # Automated gates manual [](manual_pass(n) -> <>phase(n+1)) # Manual gates next phase

[](phase(n) -> P(phase(n-1) & verified(n-1))) # 进入下一阶段前需完成上一阶段验证 [](automated_pass -> <>manual_verify) # 自动化验证通过后触发人工验证 [](manual_pass(n) -> <>phase(n+1)) # 人工验证通过后进入下一阶段

Handoff persistence

交接持久化

[](handoff_created(h) -> []exists_on_disk(h)) # Survives compaction

[](handoff_created(h) -> []exists_on_disk(h)) # 交接记录在压缩后仍保留

Termination

终止条件

<>(all_complete | abandoned)

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<>(all_complete | abandoned)

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Standard Deontic Logic (SDL)

标准道义逻辑（SDL）

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Reading obligations

读取义务

O(read_fully(plan)) O(read_fully(f)) <- mentioned_in_plan(f) O(check_existing_checkmarks) F(partial_read)

Verification obligations

验证义务

O(run_automated) <- impl_complete O(pause_for_manual) <- automated_pass O(present_manual_checklist) F(checkoff_manual) <- not user_confirmed

Mode selection

模式选择

O(orchestration) <- tasks >= 4 P(direct) <- tasks <= 3 O(respect_user_preference)

Orchestration obligations

编排义务

O(read_previous_handoff) <- exists_handoff(task_{n-1}) O(create_handoff) <- agent_completes O(update_ledger) <- task_complete F(batch_tasks) # One agent per task F(proceed_on_mismatch) <- not user_guidance

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O(read_previous_handoff) <- exists_handoff(task_{n-1}) O(create_handoff) <- agent_completes O(update_ledger) <- task_complete F(batch_tasks) # 单个任务对应单个Agent F(proceed_on_mismatch) <- not user_guidance

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Dynamic Epistemic Logic (DEL)

动态认知逻辑（DEL）

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Implementation actions

实现动作

[read(plan)]K(tasks) & K(phases) & K(criteria) [read(handoff_n)]K(context_{n+1}) [spawn(agent, task)]<>result(agent) [verify(c)](K(pass) | K(fail))

Composed workflows

组合工作流

[select_direct][implement ; verify_auto ; present_manual ; wait]* [select_orchestration][prepare ; spawn ; wait ; read_handoff ; update]*

Recovery

恢复流程

[compaction ; read_ledger ; list_handoffs ; read_last]resume

Mismatch

不匹配处理

[detect_mismatch ; stop ; present ; wait]proceed_or_abort

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[detect_mismatch ; stop ; present ; wait]proceed_or_abort

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Bridge Principles

桥接原则

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Evidence persistence (JL-TEL)

证据持久化（JL-TEL）

[h]:context(n) -> [][h]:context(n)

Evidence obligations (JL-SDL)

证据义务（JL-SDL）

O(exists h. [h]:validated) <- pre_implement O(exists v. [v]:pass(auto)) <- pre_manual

Handoff chain (full integration)

交接链（全集成）

[h_n]:complete(n) -> O([spawn]<>[h_{n+1}]:context(n+1)) compaction -> (forall h. persists(h))

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[h_n]:complete(n) -> O([spawn]<>[h_{n+1}]:context(n+1)) compaction -> (forall h. persists(h))

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State Machine

状态机

INIT --> READ_PLAN --> MODE_SELECT --+--> DIRECT: [IMPL -> AUTO -> MANUAL -> WAIT]*
                                     |
                                     +--> ORCHESTRATION: [PREP -> SPAWN -> WAIT -> HANDOFF]*
                                                                                    |
                                                                                    v
                                                                                COMPLETE

INIT --> READ_PLAN --> MODE_SELECT --+--> DIRECT: [IMPL -> AUTO -> MANUAL -> WAIT]*
                                     |
                                     +--> ORCHESTRATION: [PREP -> SPAWN -> WAIT -> HANDOFF]*
                                                                                    |
                                                                                    v
                                                                                COMPLETE

Output Schema

输出 Schema

yaml

handoff_path: "thoughts/handoffs/<session>/task-[NN]-[desc].md"
schema:
  required: [status, task_desc, files_modified[], verification_results, context_for_next]
  optional: [blocker, decisions[], open_questions[]]
tracking:
  plan: "- [x] Task N: description"
  ledger: "[x] Task N"

yaml

handoff_path: "thoughts/handoffs/<session>/task-[NN]-[desc].md"
schema:
  required: [status, task_desc, files_modified[], verification_results, context_for_next]
  optional: [blocker, decisions[], open_questions[]]
tracking:
  plan: "- [x] Task N: description"
  ledger: "[x] Task N"

Prose (Where Logic Insufficient)

补充说明（逻辑未覆盖场景）

Mode Selection

模式选择

Tasks	Context Critical	Mode
1-3	No	Direct
1-3	Yes	Orchestration
4+	Any	Orchestration

User preference overrides.

任务数量	上下文重要性	模式
1-3	否	直接模式
1-3	是	编排模式
4+	任意	编排模式

用户偏好优先级更高。

Templates

模板

Mismatch:

Issue in Phase [N]:
Expected: [plan says]
Found: [actual]
How should I proceed?

Manual Verification Pause:

Phase [N] Complete - Ready for Manual Verification
Automated passed: [list]
Please verify: [manual items from plan]
Let me know when done.

Agent Spawn:

Task(subagent_type="general-purpose", model="claude-opus-4-5-20251101", prompt="""
[implement_task SKILL.md]

不匹配提示：

第[N]阶段问题：
预期：[计划内容]
实际：[实际情况]
应如何推进？

人工验证暂停提示：

第[N]阶段完成 - 等待人工验证
自动化验证通过项：[列表]
请验证：[计划中的人工验证项]
完成后告知我。

Agent 启动模板：

Task(subagent_type="general-purpose", model="claude-opus-4-5-20251101", prompt="""
[implement_task SKILL.md]

Context

上下文

Ledger: [content]
Plan: [section]
Task: [N]/[Total]: [desc]
Previous Handoff: [content or "first task"]
Handoff Dir: thoughts/handoffs/<session>/ """)


**Recovery (post-compaction):**
1. Ledger auto-loaded by SessionStart
2. `ls thoughts/handoffs/<session>/`
3. Read last handoff
4. Resume next task

---

任务台账：[内容]
计划：[章节]
任务：[N]/[总任务数]：[描述]
上一次交接：[内容或“首个任务”]
交接目录：thoughts/handoffs/<session>/ """)


**恢复流程（压缩后）：**
1. 会话启动时自动加载任务台账
2. 执行`ls thoughts/handoffs/<session>/`
3. 读取最新的交接记录
4. 恢复下一个任务

---

Validity Constraints

有效性约束

forall phase. has_auto_criteria(phase) & has_manual_criteria(phase)
forall task. one_agent_per_task(task)
forall h. on_disk(h) -> recoverable(h)
compaction -> (forall h. persists(h))
forall i < j. completed(task_i) before started(task_j)

forall phase. has_auto_criteria(phase) & has_manual_criteria(phase)
forall task. one_agent_per_task(task)
forall h. on_disk(h) -> recoverable(h)
compaction -> (forall h. persists(h))
forall i < j. completed(task_i) before started(task_j)

implement_plan_micro

Original

Translation

Formal Specification

正式规范

Multimodal Logic Integration

多模态逻辑集成

Justification Logic (JL)

辩护逻辑（JL）

Justification terms

辩护术语

Evidence production

证据生成

Handoff chain: evidence propagates

交接链：证据传播

Inferential Erotetic Logic (IEL)

推理疑问逻辑（IEL）

Mode and blocker questions

模式与阻塞问题

Temporal Epistemic Logic (TEL)

时序认知逻辑（TEL）

File reading constraints

文件读取约束

Phase sequencing

阶段排序

Handoff persistence

交接持久化

Termination

终止条件

Standard Deontic Logic (SDL)

标准道义逻辑（SDL）

Reading obligations

读取义务

Verification obligations

验证义务

Mode selection

模式选择

Orchestration obligations

编排义务

Dynamic Epistemic Logic (DEL)

动态认知逻辑（DEL）

Implementation actions

实现动作

Composed workflows

组合工作流

Recovery

恢复流程

Mismatch

不匹配处理

Bridge Principles

桥接原则

Evidence persistence (JL-TEL)

证据持久化（JL-TEL）

Evidence obligations (JL-SDL)

证据义务（JL-SDL）

Handoff chain (full integration)

交接链（全集成）

State Machine

状态机

Output Schema

输出 Schema

Prose (Where Logic Insufficient)

补充说明（逻辑未覆盖场景）

Mode Selection

模式选择

Templates

模板

Context

上下文

Validity Constraints

有效性约束