遞歸推理樹（RR-Tree）系統：構建認知推理的骨架結構

探索基于三維評估的動態推理系統如何實現智能決策與知識演化

引言

在復雜問題求解領域（如戰略決策或科學探索），人類思維的遞歸本質為AI系統設計提供了重要啟發。我設計并實現的遞歸推理樹（Recursive Reasoning Tree, RR-Tree）系統模仿人類思維的層層推進特性，通過結構化認知過程來解決復雜問題。

本文將深入探討RR-Tree的核心機制，包括其數據結構、TQR三維評估模型和操作符引擎，并通過黑暗森林策略制定和數學反例發現兩個案例展示其實際應用。

核心數據結構：知識樹的結構化表達

RRNode：推理樹的基本單位

每個推理節點代表一個知識單元，包含以下核心屬性：

class RRNode:def __init__(self, name, content, parent=None):self.id = uuid.uuid4().hex  # 唯一標識符self.name = nameself.content = content  # 知識內容self.version = 1  # 版本迭代self.status = "hypothesized"  # 節點狀態self.tqr_score = None  # 三維質量評分self.children = []  # 子節點self.parent = parent  # 父節點

節點生命周期經歷五個階段：

hypothesized - 初步假設階段
evaluating - 質量評估階段
resolved - 已解決問題
deprecated - 被淘汰方案
merged - 與其它方案合并

RRTree：推理樹的整體架構

class RRTree:def __init__(self, root_goal):self.root = RRNode("root", root_goal)self.root.status = "active"self.evaluator = TQREvaluator()  # 質量評估器self.operator = OperatorEngine(self)  # 操作引擎self.audit_log = []  # 推理過程記錄self.converged = False  # 收斂狀態

推理樹支持從根節點開始的漸進式推理，通過reasoning_cycle()方法驅動推理循環。

TQR三維評估模型

推理質量通過三個維度進行評估：

class TQREvaluator:def evaluate(self, node, context):alpha = self._calculate_alignment(node, context)  # 邏輯連貫性beta = self._calculate_novelty(node, context)  # 觀點新穎性gamma = self._calculate_complexity(node)  # 認知復雜度# 核心評估公式numerator = alpha * (1 + beta**2)denominator = (1 + gamma)**0.5score = numerator / denominatornode.tqr_score = score

三維度詳細說明

邏輯連貫性（α）：考察節點與上下文的匹配程度
- 計算基礎分（6.0）+上下文匹配獎勵分（最高4.0）
觀點新穎性（β）：評估獨特見解的價值
- 基礎分（5.0）+獨特詞匯獎勵（每個0.1分）
認知復雜度（γ）：衡量知識深度
- 基于內容長度（詞數/20）和節點深度（深度*0.1）

操作符引擎：知識樹的演變機制

核心操作符定義了知識樹的動態演化路徑：

操作符	功能描述	狀態轉換路徑
EXPAND	擴展新分支	→ hypothesized
CHOOSE	選擇最佳子節點	evaluating → resolved
REWRITE	重構節點內容	resolved → resolved (v++)
MERGE	合并相關節點	resolved → merged
DEEP_DIVE	遞歸深入解決復雜問題	evaluating → resolved

DEEP_DIVE操作示例：

def _deep_dive(self, node):# 創建子推理樹subtree = RRTree(f"深度探索: {node.content}")# 執行遞歸推理for i in range(2):subtree.reasoning_cycle()if subtree.converged: break# 替換原節點new_node = RRNode(f"resolved_{node.name}", subtree.get_conclusion(),parent=node.parent)new_node.status = "resolved"return new_node

推理循環：認知決策的核心

推理樹通過周期性循環實現知識的漸進式演化：

def reasoning_cycle(self):current = self._select_node_to_expand()  # 選擇最佳節點if current.status in ["hypothesized", "evaluating"]:context = self._get_context(current)  # 獲取上下文self.evaluator.evaluate(current, context)  # 三維評估# 基于狀態選擇操作if self._needs_expansion(current):self.operator.apply("EXPAND", current)elif self._needs_rewrite(current):self.operator.apply("REWRITE", current)elif self._is_complex_node(current):self.operator.apply("DEEP_DIVE", current)self.converged = self._check_convergence()  # 檢查收斂

節點選擇算法：

收集所有"活動中"的邊界節點
按TQR分數降序排序
選擇最優節點進行擴展

應用案例

黑暗森林策略推導

構建宇宙文明生存策略的推理過程：

dark_forest_tree = RRTree("制定宇宙文明生存策略")# 添加公理基礎
axioms = [("axiom_1", "生存是文明第一需要"),("axiom_2", "宇宙物質總量不變"),("axiom_3", "存在其他智慧文明"),("axiom_4", "暴露位置招致毀滅風險")
]

推理路徑：

(root 制定宇宙文明生存策略)├─ (axiom_1 生存是文明第一需要)├─ (axiom_2 宇宙物質總量不變)├─ (axiom_3 存在其他智慧文明)└─ (axiom_4 暴露位置招致毀滅風險)

經過三次推理循環后，系統推導出核心策略：“保持隱匿和技術優勢以規避風險”。

數學反例發現

尋找a? + b? + c? + d? = e?的反例過程：

math_tree = RRTree("尋找a?+b?+c?+d?=e?的反例")
strategy_node = RRNode("strategy", "邊界值搜索(max=150)")
math_tree.root.add_child(strategy_node)

關鍵演變：

初始：邊界值搜索策略（max=150）
擴展出多個搜索子策略
選擇并優化TQR最高的分支
DEEP_DIVE操作生成新解決方案
結論：27? + 84? + 110? + 133? = 144?

結論與展望

RR-Tree系統通過結構化的遞歸推理實現知識的漸進式演化，其特點包括：

動態決策機制：基于TQR評分動態選擇擴展路徑
可解釋推理：完整的S表達式記錄推理過程
自適應知識演化：通過版本控制實現觀點迭代
復雜問題化解：深層遞歸分解復雜問題

未來方向：

集成大語言模型提升推理能力
引入多樹協同推理機制
開發可視化推理路徑工具
構建推理知識共享網絡

RR-Tree為復雜決策過程提供了結構化框架，將人類思維的遞歸本質轉化為可執行的算法框架，在戰略規劃、科研探索和復雜決策領域具有廣闊應用前景。

import uuid
import random
from collections import deque# ================== 核心數據結構 ==================
class RRNode:"""RR-Tree 節點實現"""def __init__(self, name, content, parent=None):self.id = uuid.uuid4().hexself.name = nameself.content = contentself.version = 1self.status = "hypothesized"  # hypothesized | evaluating | resolved | deprecated | active | mergedself.tqr_score = Noneself.children = []self.parent = parentdef add_child(self, node):"""添加子節點"""node.parent = selfself.children.append(node)return selfdef update_content(self, new_content):"""更新節點內容并增加版本號"""self.content = new_contentself.version += 1return selfdef to_s_expr(self):"""轉換為S-表達式"""children_expr = " ".join([child.to_s_expr() for child in self.children])return (f"({self.name} "f"(meta (id '{self.id}') (version {self.version}) "f"(status '{self.status}') (tqr_score {self.tqr_score or 'None'})) "f"{children_expr})")def find_node(self, node_id):"""遞歸查找節點"""if self.id == node_id:return selffor child in self.children:found = child.find_node(node_id)if found:return foundreturn Noneclass RRTree:"""完整的RR-Tree實現"""def __init__(self, root_goal):self.root = RRNode("root", root_goal)self.root.status = "active"self.evaluator = TQREvaluator()self.operator = OperatorEngine(self)self.audit_log = []self.converged = Falsedef reasoning_cycle(self):"""核心推理循環"""if self.converged:return self.rootcurrent = self._select_node_to_expand()if not current:print("沒有可擴展的節點，推理結束")self.converged = Truereturn self.rootprint(f"當前處理節點: {current.name} ({current.status}) - {current.content}")# 評估節點質量if current.status in ["hypothesized", "evaluating"]:context = self._get_context(current)print(f"評估節點: {current.name}, 上下文: {context}")self.evaluator.evaluate(current, context)print(f"評估完成 - TQR分數: {current.tqr_score:.2f}")# 應用操作符if current.children and all(c.status != "hypothesized" for c in current.children):print(f"節點 {current.name} 有子節點，執行CHOOSE操作")chosen = self.operator.apply("CHOOSE", current)print(f"選擇了節點: {chosen.name} - {chosen.content}")else:if self._needs_expansion(current):print(f"節點 {current.name} 需要擴展，執行EXPAND操作")new_nodes = self.operator.apply("EXPAND", current)print(f"新增了 {len(new_nodes)} 個子節點")elif self._needs_rewrite(current):print(f"節點 {current.name} 需要重寫，執行REWRITE操作")self.operator.apply("REWRITE", current)print(f"重寫完成: {current.content}")elif self._is_complex_node(current):print(f"節點 {current.name} 復雜，執行DEEP_DIVE操作")self.operator.apply("DEEP_DIVE", current)print(f"深度探索完成: {current.content}")# 檢查收斂條件self.converged = self._check_convergence()return self.rootdef _select_node_to_expand(self):"""基于TQR選擇最佳擴展節點"""frontier = self._get_frontier_nodes()if not frontier:# 如果沒有可擴展節點，嘗試激活根節點if self.root.status == "active":print("激活根節點進行擴展")self.root.status = "evaluating"return self.root# 或者選擇第一個子節點for child in self.root.children:if child.status in ["active", "hypothesized"]:print(f"選擇子節點 {child.name} 進行擴展")return childreturn None# 按TQR分數排序并返回最佳節點frontier.sort(key=lambda x: x.tqr_score or 0, reverse=True)best_node = frontier[0]print(f"從候選節點中選擇: {best_node.name} (分數: {best_node.tqr_score or '無'})")return best_nodedef _get_frontier_nodes(self):"""獲取所有處于活躍狀態的節點"""frontier = []queue = deque([self.root])while queue:node = queue.popleft()if node.status in ["hypothesized", "evaluating"]:frontier.append(node)queue.extend(node.children)return frontierdef _get_context(self, node):"""獲取節點上下文信息"""context = []current = nodewhile current:context.append(f"{current.name}: {current.content}")current = current.parentreturn " <- ".join(reversed(context))def _needs_expansion(self, node):"""判斷是否需要擴展"""return len(node.children) < 3 and (node.tqr_score or 0) > 0def _needs_rewrite(self, node):"""判斷是否需要重寫"""if node.status != "resolved":return Falsereturn (node.tqr_score or 0) < 7.0 and node.version < 3def _is_complex_node(self, node):"""判斷是否需要深度遞歸"""return ((node.tqr_score or 0) > 7.0and self.evaluator._calculate_complexity(node) > 5.0)def _check_convergence(self):"""檢查樹是否收斂（所有節點已解決或棄用）"""queue = deque([self.root])while queue:node = queue.popleft()if node.status not in ["resolved", "deprecated", "active", "merged"]:return Falsequeue.extend(node.children)return Truedef find_node(self, node_id):"""在樹中查找節點"""return self.root.find_node(node_id)def to_s_expr(self):"""將整棵樹轉換為S-表達式"""return self.root.to_s_expr()def get_conclusion(self):"""獲取最終結論（根節點的第一個已解決子節點）"""if self.converged:for child in self.root.children:if child.status == "resolved":return child.contentreturn "未達成結論"# ================== TQR評估模型 ==================
class TQREvaluator:"""TQR評估引擎"""def __init__(self, alpha_weight=1.0, beta_weight=1.5, gamma_weight=0.7):self.weights = {'alpha': alpha_weight, 'beta': beta_weight, 'gamma': gamma_weight}def evaluate(self, node, context):"""三維度評估節點質量"""alpha = self._calculate_alignment(node, context)beta = self._calculate_novelty(node, context)gamma = self._calculate_complexity(node)# 核心公式: TQR = (α * (1 + β2)) / (1 + γ)^0.5numerator = self.weights['alpha'] * alpha * (1 + (self.weights['beta'] * beta) ** 2)denominator = (1 + self.weights['gamma'] * gamma) ** 0.5score = numerator / denominator if denominator != 0 else numeratornode.tqr_score = scorereturn scoredef _calculate_alignment(self, node, context):"""邏輯連貫性評估"""# 簡化實現：基于上下文匹配度context_words = set(word for word in context.split() if len(word) > 3)node_words = set(word for word in node.content.split() if len(word) > 3)intersection = context_words & node_words# 基本分數 + 匹配度加分base_score = 6.0  # 中等分數match_bonus = min(len(intersection) * 0.5, 4.0)  # 最高加4分return base_score + match_bonusdef _calculate_novelty(self, node, context):"""新穎性評估"""# 簡化實現：基于獨特詞匯unique_words = set(node.content.split()) - set(context.split())uniqueness = len(unique_words) / 10  # 每個獨特詞匯加0.1分# 基本分數 + 獨特性加分base_score = 5.0return min(base_score + uniqueness, 10.0)def _calculate_complexity(self, node):"""認知復雜度評估"""# 基于內容長度和嵌套深度word_count = len(node.content.split())depth = self._get_node_depth(node)complexity = word_count / 20 + depth * 0.1return min(complexity, 10.0)def _get_node_depth(self, node):"""計算節點在樹中的深度"""depth = 0current = nodewhile current.parent:depth += 1current = current.parentreturn depth# ================== 操作符引擎 ==================
class OperatorEngine:"""操作符執行引擎"""def __init__(self, tree):self.tree = treeself.state_transitions = {"EXPAND": {"from": ["active", "resolved", "evaluating"], "to": "hypothesized"},"CHOOSE": {"from": "evaluating", "to": "resolved"},"REWRITE": {"from": ["resolved", "active"], "to": "resolved"},"MERGE": {"from": "resolved", "to": "merged"},"DEEP_DIVE": {"from": ["evaluating", "active"], "to": "resolved"}}def apply(self, operator, target, params=None):"""應用操作符"""if isinstance(target, str):node = self.tree.find_node(target)else:node = targetif not node:print(f"目標節點未找到: {target}")return None# 檢查狀態轉換是否有效valid_states = self.state_transitions.get(operator, {}).get("from", [])if node.status not in valid_states:print(f"無效狀態轉換: 無法在狀態 {node.status} 下應用 {operator}")return nodeif operator == "EXPAND":return self._expand(node)elif operator == "CHOOSE":return self._choose(node)elif operator == "REWRITE":return self._rewrite(node)elif operator == "MERGE":return self._merge(node, params.get('sibling_nodes', []) if params else [])elif operator == "DEEP_DIVE":return self._deep_dive(node)else:print(f"未知操作符: {operator}")return nodedef _expand(self, node):"""EXPAND操作實現"""# 生成子節點內容expansions = [f"關于'{node.content}'的深入分析",f"對'{node.content}'的補充觀點",f"'{node.content}'的實際應用"]new_nodes = []for i, content in enumerate(expansions):child = RRNode(f"{node.name}_child_{i + 1}", content, parent=node)child.status = "hypothesized"node.add_child(child)new_nodes.append(child)node.status = "evaluating"return new_nodesdef _choose(self, parent_node):"""CHOOSE操作實現"""if not parent_node.children:print(f"節點 {parent_node.name} 沒有子節點可供選擇")return None# 選擇TQR分數最高的子節點best_child = max(parent_node.children, key=lambda x: x.tqr_score or 0)# 更新所有子節點狀態for child in parent_node.children:child.status = "deprecated" if child != best_child else "resolved"parent_node.status = "resolved"return best_childdef _rewrite(self, node):"""REWRITE操作實現"""# 改進節點內容improved_content = f"[v{node.version + 1}] 改進版: {node.content}"node.update_content(improved_content)return nodedef _merge(self, target_node, sibling_nodes):"""MERGE操作實現"""# 收集所有需要合并的節點all_nodes = [target_node] + sibling_nodes# 創建新父節點parent_content = f"合并觀點: {', '.join(n.content for n in all_nodes)}"new_parent = RRNode(f"merged_{target_node.name}", parent_content, parent=target_node.parent)# 重新設置父關系for node in all_nodes:node.parent = new_parentnode.status = "merged"new_parent.children.append(node)# 在樹結構中替換節點if target_node.parent:target_node.parent.children.remove(target_node)target_node.parent.add_child(new_parent)return new_parentdef _deep_dive(self, node):"""DEEP_DIVE遞歸操作"""# 創建子推理樹subtree = RRTree(f"深度探索: {node.content}")# 添加初始節點start_node = RRNode("deep_start", "開始探索", parent=subtree.root)subtree.root.add_child(start_node)# 執行子推理過程for i in range(2):  # 簡化：執行2個推理周期subtree.reasoning_cycle()if subtree.converged:break# 創建新節點替換原節點new_content = subtree.get_conclusion()new_node = RRNode(f"resolved_{node.name}",new_content,parent=node.parent)new_node.status = "resolved"# 在樹結構中替換節點if node.parent:node.parent.children.remove(node)node.parent.add_child(new_node)return new_node# ================== 使用示例 ==================
if __name__ == "__main__":print("===== 黑暗森林策略推理 =====")# 創建推理樹 - 黑暗森林策略dark_forest_tree = RRTree("制定宇宙文明生存策略")# 添加公理節點axioms = [("axiom_1", "生存是文明第一需要"),("axiom_2", "宇宙物質總量不變"),("axiom_3", "存在其他智慧文明"),("axiom_4", "暴露位置招致毀滅風險")]for name, content in axioms:node = RRNode(name, content)node.status = "active"dark_forest_tree.root.add_child(node)print("\n===== 初始狀態 =====")print(dark_forest_tree.to_s_expr())# 執行推理循環for i in range(3):print(f"\n===== 推理周期 {i + 1} =====")dark_forest_tree.reasoning_cycle()print(dark_forest_tree.to_s_expr())# 最終結論print("\n===== 最終結論 =====")print(dark_forest_tree.get_conclusion())print("\n\n===== 數學反例發現 =====")# 數學反例發現math_tree = RRTree("尋找a?+b?+c?+d?=e?的反例")math_tree.evaluator.weights = {'alpha': 1.2, 'beta': 2.0, 'gamma': 0.5}strategy_node = RRNode("strategy", "邊界值搜索(max=150)")strategy_node.status = "active"math_tree.root.add_child(strategy_node)for i in range(3):print(f"\n===== 推理周期 {i + 1} =====")math_tree.reasoning_cycle()print(math_tree.to_s_expr())print("\n===== 數學反例 =====")print(math_tree.get_conclusion())