C7-1 本体论地位推论 - 形式化描述
1. 形式化框架
1.1 本体论地位系统模型
class OntologicalStatusSystem:
"""C7-1本体论地位推论的数学模型"""
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
self.max_levels = 10 # 实际可构造的最大层级数
self.entity_cache = {} # 缓存实体信息
self.level_cache = {} # 缓存层级结构
self.dependency_graph = {} # 依赖关系图
self.existence_proofs = {} # 存在证明缓存
def create_ontological_levels(self, max_level: int) -> Dict[str, Any]:
"""创建本体论存在层级"""
levels = {
'level_count': max_level,
'levels': [],
'level_mapping': {},
'consistency_verified': False
}
for level_num in range(max_level):
level_info = {
'level': level_num,
'name': f'Level_{level_num}',
'entities': self._generate_level_entities(level_num),
'construction_rules': self._get_construction_rules(level_num),
'existence_axioms': self._get_existence_axioms(level_num),
'dependency_relations': {}
}
levels['levels'].append(level_info)
levels['level_mapping'][f'Level_{level_num}'] = level_info
# 建立依赖关系
self._establish_dependency_relations(levels)
# 验证层级一致性
levels['consistency_verified'] = self._verify_level_consistency(levels)
return levels
def _generate_level_entities(self, level: int) -> List[Dict[str, Any]]:
"""生成指定层级的实体"""
entities = []
if level == 0:
# 基础层级：不含自指的基本实体
for i in range(8):
entity_encoding = format(i, '03b')
if '11' not in entity_encoding: # 满足no-11约束
entity = {
'id': f'base_entity_{entity_encoding}',
'encoding': entity_encoding,
'type': 'basic',
'self_reference_level': 0,
'construction_dependencies': []
}
entities.append(entity)
else:
# 高层级：通过构造函子从低层级构造
base_count = 4 # 每层级的基础实体数
for i in range(base_count):
# 构造复杂实体
dependencies = self._select_dependencies(level - 1)
entity_encoding = self._construct_entity_encoding(level, i, dependencies)
if '11' not in entity_encoding:
entity = {
'id': f'constructed_entity_L{level}_{i}',
'encoding': entity_encoding,
'type': 'constructed',
'level': level,
'self_reference_level': self._calculate_self_ref_level(dependencies),
'construction_dependencies': dependencies
}
entities.append(entity)
return entities
def _select_dependencies(self, from_level: int) -> List[str]:
"""从指定层级选择依赖实体"""
# 简化的依赖选择：每个实体依赖于前一层级的1-2个实体
dependencies = []
dependency_count = min(2, from_level + 1)
for i in range(dependency_count):
dep_encoding = format(i, '03b')
if '11' not in dep_encoding:
dependencies.append(f'entity_L{from_level}_{dep_encoding}')
return dependencies
def _construct_entity_encoding(self, level: int, index: int, dependencies: List[str]) -> str:
"""构造实体的二进制编码"""
# 层级前缀
level_prefix = format(level, '03b')
# 索引编码
index_encoding = format(index, '03b')
# 依赖哈希
dep_hash = abs(hash(str(dependencies))) % (2**4)
dep_encoding = format(dep_hash, '04b')
# 合并编码
full_encoding = level_prefix + index_encoding + dep_encoding
# 确保no-11约束
while '11' in full_encoding:
full_encoding = full_encoding.replace('11', '10')
return full_encoding
def _calculate_self_ref_level(self, dependencies: List[str]) -> int:
"""计算自指层级"""
# 简化计算：基于依赖数量
return len(dependencies)
def _get_construction_rules(self, level: int) -> List[Dict[str, Any]]:
"""获取构造规则"""
rules = []
if level == 0:
# 基础层级的公理规则
rules.append({
'type': 'axiom',
'name': 'basic_existence',
'rule': 'base entities exist axiomatically',
'formula': '⊢ Exists(e) for all e ∈ Level_0'
})
else:
# 构造规则
rules.append({
'type': 'construction',
'name': 'recursive_construction',
'rule': 'construct from lower levels',
'formula': f'Exists(e₁),...,Exists(eₙ) ⊢ Exists(F(e₁,...,eₙ))'
})
return rules
def _get_existence_axioms(self, level: int) -> List[str]:
"""获取存在公理"""
axioms = []
if level == 0:
axioms.append('∀e ∈ Level_0: ⊢ Exists(e)')
else:
axioms.append(f'∀e ∈ Level_{level}: ∃π: π ⊢ Exists(e)')
return axioms
def _establish_dependency_relations(self, levels: Dict[str, Any]) -> None:
"""建立依赖关系"""
for level_info in levels['levels']:
level_num = level_info['level']
for entity in level_info['entities']:
entity_id = entity['id']
dependencies = entity.get('construction_dependencies', [])
# 建立依赖关系
if dependencies:
for dep in dependencies:
if entity_id not in self.dependency_graph:
self.dependency_graph[entity_id] = []
self.dependency_graph[entity_id].append(dep)
# 在层级中记录依赖
if 'dependents' not in level_info['dependency_relations']:
level_info['dependency_relations']['dependents'] = {}
level_info['dependency_relations']['dependents'][entity_id] = dependencies
def _verify_level_consistency(self, levels: Dict[str, Any]) -> bool:
"""验证层级一致性"""
# 检查是否存在循环依赖
if self._has_circular_dependencies():
return False
# 检查层级分离
if not self._verify_level_separation(levels):
return False
# 检查构造规则的有效性
if not self._verify_construction_rules(levels):
return False
return True
def _has_circular_dependencies(self) -> bool:
"""检查是否存在循环依赖"""
visited = set()
path = set()
def dfs(node):
if node in path:
return True # 发现循环
if node in visited:
return False
visited.add(node)
path.add(node)
for neighbor in self.dependency_graph.get(node, []):
if dfs(neighbor):
return True
path.remove(node)
return False
for node in self.dependency_graph:
if node not in visited:
if dfs(node):
return True
return False
def _verify_level_separation(self, levels: Dict[str, Any]) -> bool:
"""验证层级分离"""
# 检查高层级实体不依赖于同层级或更高层级实体
for level_info in levels['levels']:
level_num = level_info['level']
for entity in level_info['entities']:
dependencies = entity.get('construction_dependencies', [])
for dep in dependencies:
# 提取依赖实体的层级
dep_level = self._extract_entity_level(dep)
if dep_level >= level_num:
return False # 违反层级分离
return True
def _extract_entity_level(self, entity_id: str) -> int:
"""从实体ID提取层级信息"""
# 简化提取：从ID中解析层级
if 'base_entity' in entity_id:
return 0
elif '_L' in entity_id:
try:
level_part = entity_id.split('_L')[1].split('_')[0]
return int(level_part)
except:
return 0
return 0
def _verify_construction_rules(self, levels: Dict[str, Any]) -> bool:
"""验证构造规则的有效性"""
# 检查每个构造规则是否正确应用
for level_info in levels['levels']:
rules = level_info['construction_rules']
for rule in rules:
if rule['type'] == 'construction':
# 验证构造规则的一致性
if not self._validate_construction_rule(rule, level_info):
return False
return True
def _validate_construction_rule(self, rule: Dict[str, Any], level_info: Dict[str, Any]) -> bool:
"""验证单个构造规则"""
# 简化验证：检查规则格式的正确性
required_fields = ['type', 'name', 'rule', 'formula']
return all(field in rule for field in required_fields)
def construct_existence_proof(self, entity_id: str, levels: Dict[str, Any]) -> Dict[str, Any]:
"""构造实体的存在证明"""
proof = {
'entity': entity_id,
'proof_found': False,
'proof_steps': [],
'proof_encoding': None,
'dependencies_satisfied': False
}
# 查找实体
entity = self._find_entity(entity_id, levels)
if not entity:
return proof
# 构造证明步骤
proof_steps = []
# 如果是基础实体，直接应用公理
if entity['type'] == 'basic':
proof_steps.append({
'step': 1,
'type': 'axiom',
'statement': f'Exists({entity_id})',
'justification': 'Basic existence axiom'
})
proof['dependencies_satisfied'] = True
else:
# 构造性实体需要递归证明依赖
dependencies = entity.get('construction_dependencies', [])
step_num = 1
# 首先证明所有依赖实体的存在
for dep in dependencies:
dep_proof = self.construct_existence_proof(dep, levels)
if not dep_proof['proof_found']:
return proof # 依赖证明失败
proof_steps.append({
'step': step_num,
'type': 'dependency',
'statement': f'Exists({dep})',
'justification': f'From dependency proof'
})
step_num += 1
# 应用构造规则
proof_steps.append({
'step': step_num,
'type': 'construction',
'statement': f'Exists({entity_id})',
'justification': f'Construction rule applied to dependencies'
})
proof['dependencies_satisfied'] = True
proof['proof_steps'] = proof_steps
proof['proof_found'] = True
# 编码证明
proof_encoding = self._encode_proof(proof_steps)
proof['proof_encoding'] = proof_encoding
return proof
def _find_entity(self, entity_id: str, levels: Dict[str, Any]) -> Dict[str, Any]:
"""查找指定实体"""
for level_info in levels['levels']:
for entity in level_info['entities']:
if entity['id'] == entity_id:
return entity
return None
def _encode_proof(self, proof_steps: List[Dict[str, Any]]) -> str:
"""编码证明步骤"""
# 简化编码：基于步骤数量和类型
step_count = len(proof_steps)
step_types = [step['type'] for step in proof_steps]
# 生成编码
count_encoding = format(step_count, '04b')
type_hash = abs(hash(str(step_types))) % (2**8)
type_encoding = format(type_hash, '08b')
full_encoding = count_encoding + type_encoding
# 确保no-11约束
while '11' in full_encoding:
full_encoding = full_encoding.replace('11', '10')
return full_encoding
def analyze_dependency_relations(self, levels: Dict[str, Any]) -> Dict[str, Any]:
"""分析依赖关系"""
analysis = {
'total_entities': 0,
'total_dependencies': 0,
'dependency_matrix': {},
'transitivity_verified': False,
'acyclicity_verified': False,
'level_consistency_verified': False
}
# 统计基本信息
for level_info in levels['levels']:
analysis['total_entities'] += len(level_info['entities'])
for entity in level_info['entities']:
dependencies = entity.get('construction_dependencies', [])
analysis['total_dependencies'] += len(dependencies)
# 构造依赖矩阵
entity_id = entity['id']
analysis['dependency_matrix'][entity_id] = dependencies
# 验证传递性
analysis['transitivity_verified'] = self._verify_transitivity(analysis['dependency_matrix'])
# 验证无环性
analysis['acyclicity_verified'] = not self._has_circular_dependencies()
# 验证层级一致性
analysis['level_consistency_verified'] = self._verify_dependency_level_consistency(levels)
return analysis
def _verify_transitivity(self, dependency_matrix: Dict[str, List[str]]) -> bool:
"""验证依赖关系的传递性"""
# 构造传递闭包
transitive_closure = {}
# 初始化
for entity, deps in dependency_matrix.items():
transitive_closure[entity] = set(deps)
# Floyd-Warshall算法计算传递闭包
entities = list(dependency_matrix.keys())
for k in entities:
for i in entities:
for j in entities:
if k in transitive_closure.get(i, set()) and j in transitive_closure.get(k, set()):
if i not in transitive_closure:
transitive_closure[i] = set()
transitive_closure[i].add(j)
# 验证传递性：如果A依赖B，B依赖C，则A应该（间接）依赖C
for entity, direct_deps in dependency_matrix.items():
transitive_deps = transitive_closure.get(entity, set())
for dep in direct_deps:
dep_deps = transitive_closure.get(dep, set())
if not dep_deps.issubset(transitive_deps):
return False
return True
def _verify_dependency_level_consistency(self, levels: Dict[str, Any]) -> bool:
"""验证依赖关系与层级的一致性"""
for level_info in levels['levels']:
level_num = level_info['level']
for entity in level_info['entities']:
dependencies = entity.get('construction_dependencies', [])
for dep in dependencies:
dep_level = self._extract_entity_level(dep)
# 依赖实体必须在更低的层级
if dep_level >= level_num:
return False
return True
def verify_self_reference_status(self, levels: Dict[str, Any]) -> Dict[str, Any]:
"""验证自指系统的特殊地位"""
verification = {
'self_reference_entity': None,
'highest_level': 0,
'self_foundation_verified': False,
'complete_generation_verified': False,
'self_proof_verified': False
}
# 查找自指实体（最高层级）
max_level = -1
self_ref_entity = None
for level_info in levels['levels']:
level_num = level_info['level']
if level_num > max_level:
max_level = level_num
# 查找最复杂的自指实体
for entity in level_info['entities']:
if entity.get('self_reference_level', 0) > 0:
self_ref_entity = entity
verification['highest_level'] = max_level
verification['self_reference_entity'] = self_ref_entity
if self_ref_entity:
# 验证自基础性
verification['self_foundation_verified'] = self._verify_self_foundation(self_ref_entity)
# 验证完备生成性
verification['complete_generation_verified'] = self._verify_complete_generation(self_ref_entity, levels)
# 验证自证明
verification['self_proof_verified'] = self._verify_self_proof(self_ref_entity)
return verification
def _verify_self_foundation(self, self_ref_entity: Dict[str, Any]) -> bool:
"""验证自指实体的自基础性"""
# 简化验证：检查自指实体是否在其自己的依赖中
entity_id = self_ref_entity['id']
dependencies = self_ref_entity.get('construction_dependencies', [])
# 自基础性体现为某种形式的自包含
return len(dependencies) > 0 and self_ref_entity.get('self_reference_level', 0) > 0
def _verify_complete_generation(self, self_ref_entity: Dict[str, Any], levels: Dict[str, Any]) -> bool:
"""验证完备生成性"""
# 简化验证：检查是否所有实体都可以从自指实体推导
# 在实际实现中，这需要构造完整的推导树
total_entities = sum(len(level_info['entities']) for level_info in levels['levels'])
# 假设自指实体可以生成大部分其他实体
return total_entities > 1 # 简化判断
def _verify_self_proof(self, self_ref_entity: Dict[str, Any]) -> bool:
"""验证自证明"""
# 自指实体应该能够证明自己的存在
entity_id = self_ref_entity['id']
# 简化验证：自指实体的存在性是自明的
return self_ref_entity.get('type') == 'constructed' and self_ref_entity.get('self_reference_level', 0) > 0
def check_existence_completeness(self, levels: Dict[str, Any]) -> Dict[str, Any]:
"""检查存在完备性"""
completeness_check = {
'total_possible_entities': 0,
'included_entities': 0,
'excluded_entities': 0,
'completeness_rate': 0.0,
'decidability_verified': False,
'level_completeness': {}
}
# 估计可能存在的实体数量（基于no-11约束）
max_encoding_length = 10 # 假设最大编码长度
total_possible = 0
for length in range(1, max_encoding_length + 1):
# 计算长度为length且满足no-11约束的二进制串数量
possible_count = self._count_no11_strings(length)
total_possible += possible_count
completeness_check['total_possible_entities'] = total_possible
# 统计实际包含的实体
included_count = 0
for level_info in levels['levels']:
level_entities = len(level_info['entities'])
included_count += level_entities
completeness_check['level_completeness'][f"Level_{level_info['level']}"] = {
'entity_count': level_entities,
'completeness_rate': level_entities / max(1, total_possible // levels['level_count'])
}
completeness_check['included_entities'] = included_count
completeness_check['excluded_entities'] = max(0, total_possible - included_count)
if total_possible > 0:
completeness_check['completeness_rate'] = included_count / total_possible
# 验证可决定性
completeness_check['decidability_verified'] = self._verify_existence_decidability(levels)
return completeness_check
def _count_no11_strings(self, length: int) -> int:
"""计算指定长度的no-11约束二进制串数量"""
if length <= 0:
return 0
if length == 1:
return 2 # '0', '1'
if length == 2:
return 3 # '00', '01', '10' (排除'11')
# 动态规划计算
dp = [0] * (length + 1)
dp[0] = 1
dp[1] = 2
for i in range(2, length + 1):
dp[i] = dp[i-1] + dp[i-2] # Fibonacci-like sequence
return dp[length]
def _verify_existence_decidability(self, levels: Dict[str, Any]) -> bool:
"""验证存在的可决定性"""
# 简化验证：检查是否每个实体都有明确的存在证明或不存在证明
for level_info in levels['levels']:
for entity in level_info['entities']:
entity_id = entity['id']
# 尝试构造存在证明
proof = self.construct_existence_proof(entity_id, levels)
# 如果无法构造证明，可决定性验证失败
if not proof['proof_found']:
return False
return True
def run_comprehensive_verification(self, max_level: int = 5) -> Dict[str, Any]:
"""运行完整的本体论地位验证"""
results = {
'ontological_levels': {},
'existence_proofs': {},
'dependency_analysis': {},
'self_reference_verification': {},
'completeness_check': {},
'overall_assessment': {}
}
# 1. 创建本体论层级
levels = self.create_ontological_levels(max_level)
results['ontological_levels'] = levels
# 2. 构造存在证明
proof_results = {}
if levels['consistency_verified']:
for level_info in levels['levels']:
for entity in level_info['entities'][:2]: # 限制测试实体数量
entity_id = entity['id']
proof = self.construct_existence_proof(entity_id, levels)
proof_results[entity_id] = proof
results['existence_proofs'] = proof_results
# 3. 分析依赖关系
dependency_analysis = self.analyze_dependency_relations(levels)
results['dependency_analysis'] = dependency_analysis
# 4. 验证自指地位
self_ref_verification = self.verify_self_reference_status(levels)
results['self_reference_verification'] = self_ref_verification
# 5. 检查完备性
completeness_check = self.check_existence_completeness(levels)
results['completeness_check'] = completeness_check
# 6. 总体评估
results['overall_assessment'] = self._assess_ontological_status(results)
return results
def _assess_ontological_status(self, results: Dict[str, Any]) -> Dict[str, Any]:
"""评估本体论地位系统的整体状况"""
assessment = {
'level_construction_verified': False,
'existence_proof_verified': False,
'dependency_consistency_verified': False,
'self_reference_verified': False,
'completeness_verified': False,
'overall_status': 'Failed'
}
# 评估层级构造
levels = results.get('ontological_levels', {})
if levels.get('consistency_verified', False) and levels.get('level_count', 0) > 0:
assessment['level_construction_verified'] = True
# 评估存在证明
proofs = results.get('existence_proofs', {})
if proofs:
proof_success_rate = sum(1 for p in proofs.values() if p.get('proof_found', False)) / len(proofs)
if proof_success_rate > 0.8:
assessment['existence_proof_verified'] = True
# 评估依赖一致性
dependency_analysis = results.get('dependency_analysis', {})
if (dependency_analysis.get('transitivity_verified', False) and
dependency_analysis.get('acyclicity_verified', False) and
dependency_analysis.get('level_consistency_verified', False)):
assessment['dependency_consistency_verified'] = True
# 评估自指验证
self_ref = results.get('self_reference_verification', {})
if (self_ref.get('self_foundation_verified', False) and
self_ref.get('complete_generation_verified', False)):
assessment['self_reference_verified'] = True
# 评估完备性
completeness = results.get('completeness_check', {})
if (completeness.get('completeness_rate', 0) > 0.1 and
completeness.get('decidability_verified', False)):
assessment['completeness_verified'] = True
# 总体评估
verified_count = sum([
assessment['level_construction_verified'],
assessment['existence_proof_verified'],
assessment['dependency_consistency_verified'],
assessment['self_reference_verified'],
assessment['completeness_verified']
])
if verified_count >= 4:
assessment['overall_status'] = 'Strong'
elif verified_count >= 3:
assessment['overall_status'] = 'Moderate'
elif verified_count >= 2:
assessment['overall_status'] = 'Weak'
return assessment
1.2 存在层级分析器
class ExistenceLevelAnalyzer:
"""存在层级的详细分析"""
def __init__(self):
self.oss = OntologicalStatusSystem()
self.phi = (1 + np.sqrt(5)) / 2
def analyze_existence_hierarchy(self, levels: Dict[str, Any]) -> Dict[str, Any]:
"""分析存在层级结构"""
analysis = {
'level_structure': {},
'complexity_analysis': {},
'reduction_analysis': {},
'classification_analysis': {}
}
# 分析层级结构
analysis['level_structure'] = self._analyze_level_structure(levels)
# 分析复杂度
analysis['complexity_analysis'] = self._analyze_complexity(levels)
# 分析还原关系
analysis['reduction_analysis'] = self._analyze_reduction_relations(levels)
# 分析存在分类
analysis['classification_analysis'] = self._analyze_existence_classification(levels)
return analysis
def _analyze_level_structure(self, levels: Dict[str, Any]) -> Dict[str, Any]:
"""分析层级结构"""
structure = {
'level_count': levels.get('level_count', 0),
'entities_per_level': {},
'level_dependencies': {},
'hierarchy_depth': 0
}
max_level = -1
for level_info in levels.get('levels', []):
level_num = level_info['level']
entity_count = len(level_info['entities'])
structure['entities_per_level'][f'Level_{level_num}'] = entity_count
# 分析层级依赖
dependencies = set()
for entity in level_info['entities']:
entity_deps = entity.get('construction_dependencies', [])
for dep in entity_deps:
dep_level = self.oss._extract_entity_level(dep)
dependencies.add(dep_level)
structure['level_dependencies'][f'Level_{level_num}'] = list(dependencies)
max_level = max(max_level, level_num)
structure['hierarchy_depth'] = max_level + 1
return structure
def _analyze_complexity(self, levels: Dict[str, Any]) -> Dict[str, Any]:
"""分析存在复杂度"""
complexity = {
'complexity_by_level': {},
'average_complexity': 0.0,
'complexity_growth_rate': 0.0
}
total_complexity = 0
entity_count = 0
for level_info in levels.get('levels', []):
level_num = level_info['level']
level_complexity = []
for entity in level_info['entities']:
# 计算实体复杂度
entity_complexity = self._calculate_entity_complexity(entity, level_num)
level_complexity.append(entity_complexity)
total_complexity += entity_complexity
entity_count += 1
complexity['complexity_by_level'][f'Level_{level_num}'] = {
'average': sum(level_complexity) / len(level_complexity) if level_complexity else 0,
'max': max(level_complexity) if level_complexity else 0,
'min': min(level_complexity) if level_complexity else 0
}
if entity_count > 0:
complexity['average_complexity'] = total_complexity / entity_count
# 计算增长率
if len(levels.get('levels', [])) > 1:
complexity['complexity_growth_rate'] = self._calculate_growth_rate(complexity['complexity_by_level'])
return complexity
def _calculate_entity_complexity(self, entity: Dict[str, Any], level: int) -> float:
"""计算单个实体的复杂度"""
base_complexity = 1.0
# 层级贡献
level_factor = level * self.phi**level
# 依赖贡献
dependencies = entity.get('construction_dependencies', [])
dependency_factor = len(dependencies)
# 自指贡献
self_ref_level = entity.get('self_reference_level', 0)
self_ref_factor = self_ref_level * 2
# 编码长度贡献
encoding = entity.get('encoding', '')
encoding_factor = len(encoding)
total_complexity = base_complexity + level_factor + dependency_factor + self_ref_factor + encoding_factor
return total_complexity
def _calculate_growth_rate(self, complexity_by_level: Dict[str, Dict[str, float]]) -> float:
"""计算复杂度增长率"""
levels = sorted(complexity_by_level.keys())
if len(levels) < 2:
return 0.0
complexities = [complexity_by_level[level]['average'] for level in levels]
# 计算平均增长率
growth_rates = []
for i in range(1, len(complexities)):
if complexities[i-1] > 0:
growth_rate = (complexities[i] - complexities[i-1]) / complexities[i-1]
growth_rates.append(growth_rate)
return sum(growth_rates) / len(growth_rates) if growth_rates else 0.0
def _analyze_reduction_relations(self, levels: Dict[str, Any]) -> Dict[str, Any]:
"""分析还原关系"""
reduction = {
'reduction_map': {},
'irreducible_entities': [],
'reduction_depth': {},
'reduction_completeness': 0.0
}
# 分析每个实体的还原关系
for level_info in levels.get('levels', []):
level_num = level_info['level']
for entity in level_info['entities']:
entity_id = entity['id']
dependencies = entity.get('construction_dependencies', [])
if dependencies:
# 可还原实体
reduction['reduction_map'][entity_id] = dependencies
# 计算还原深度
depth = self._calculate_reduction_depth(entity_id, levels)
reduction['reduction_depth'][entity_id] = depth
else:
# 不可还原实体
reduction['irreducible_entities'].append(entity_id)
# 计算还原完备性
total_entities = sum(len(level_info['entities']) for level_info in levels.get('levels', []))
reducible_entities = len(reduction['reduction_map'])
if total_entities > 0:
reduction['reduction_completeness'] = reducible_entities / total_entities
return reduction
def _calculate_reduction_depth(self, entity_id: str, levels: Dict[str, Any]) -> int:
"""计算还原深度"""
visited = set()
def dfs(current_id):
if current_id in visited:
return 0 # 避免循环
visited.add(current_id)
# 找到当前实体
current_entity = None
for level_info in levels.get('levels', []):
for entity in level_info['entities']:
if entity['id'] == current_id:
current_entity = entity
break
if current_entity:
break
if not current_entity:
return 0
dependencies = current_entity.get('construction_dependencies', [])
if not dependencies:
return 1 # 基础实体
# 计算最大深度
max_depth = 0
for dep in dependencies:
dep_depth = dfs(dep)
max_depth = max(max_depth, dep_depth)
return max_depth + 1
return dfs(entity_id)
def _analyze_existence_classification(self, levels: Dict[str, Any]) -> Dict[str, Any]:
"""分析存在分类"""
classification = {
'type_distribution': {},
'classification_criteria': {},
'type_count': 0
}
# 统计实体类型分布
type_counts = {}
for level_info in levels.get('levels', []):
for entity in level_info['entities']:
entity_type = entity.get('type', 'unknown')
type_counts[entity_type] = type_counts.get(entity_type, 0) + 1
classification['type_distribution'] = type_counts
classification['type_count'] = len(type_counts)
# 定义分类标准
classification['classification_criteria'] = {
'basic': 'No construction dependencies',
'constructed': 'Has construction dependencies',
'self_referential': 'Self-reference level > 0',
'complex': 'Multiple dependencies and high complexity'
}
return classification
def measure_ontological_quality(self, levels: Dict[str, Any]) -> Dict[str, Any]:
"""测量本体论质量"""
quality_metrics = {
'structural_quality': 0.0,
'completeness_quality': 0.0,
'consistency_quality': 0.0,
'efficiency_quality': 0.0,
'overall_quality': 0.0
}
# 结构质量
structure_analysis = self._analyze_level_structure(levels)
if structure_analysis['hierarchy_depth'] > 0:
level_balance = self._calculate_level_balance(structure_analysis)
quality_metrics['structural_quality'] = min(1.0, level_balance)
# 完备性质量
completeness_check = self.oss.check_existence_completeness(levels)
quality_metrics['completeness_quality'] = completeness_check.get('completeness_rate', 0.0)
# 一致性质量
if levels.get('consistency_verified', False):
quality_metrics['consistency_quality'] = 1.0
# 效率质量
complexity_analysis = self._analyze_complexity(levels)
avg_complexity = complexity_analysis.get('average_complexity', 0.0)
if avg_complexity > 0:
quality_metrics['efficiency_quality'] = min(1.0, 10.0 / avg_complexity)
# 总体质量
quality_metrics['overall_quality'] = (
quality_metrics['structural_quality'] * 0.3 +
quality_metrics['completeness_quality'] * 0.3 +
quality_metrics['consistency_quality'] * 0.2 +
quality_metrics['efficiency_quality'] * 0.2
)
return quality_metrics
def _calculate_level_balance(self, structure_analysis: Dict[str, Any]) -> float:
"""计算层级平衡度"""
entities_per_level = structure_analysis['entities_per_level']
if not entities_per_level:
return 0.0
counts = list(entities_per_level.values())
if len(counts) <= 1:
return 1.0
# 计算变异系数
mean_count = sum(counts) / len(counts)
if mean_count == 0:
return 0.0
variance = sum((c - mean_count)**2 for c in counts) / len(counts)
std_dev = variance**0.5
coefficient_of_variation = std_dev / mean_count
# 转换为质量分数（越低越好）
balance_score = max(0.0, 1.0 - coefficient_of_variation)
return balance_score
1.3 本体论地位验证器
class OntologicalStatusVerifier:
"""C7-1本体论地位推论的综合验证"""
def __init__(self):
self.oss = OntologicalStatusSystem()
self.ela = ExistenceLevelAnalyzer()
def run_comprehensive_verification(self, max_level: int = 4) -> Dict[str, Any]:
"""运行完整验证套件"""
results = {
'ontological_level_verification': {},
'existence_proof_verification': {},
'dependency_relation_verification': {},
'self_reference_verification': {},
'completeness_verification': {},
'overall_assessment': {}
}
# 1. 验证本体论层级构造
level_verification = self._verify_ontological_levels(max_level)
results['ontological_level_verification'] = level_verification
# 2. 验证存在证明
proof_verification = self._verify_existence_proofs(level_verification['levels'])
results['existence_proof_verification'] = proof_verification
# 3. 验证依赖关系
dependency_verification = self._verify_dependency_relations(level_verification['levels'])
results['dependency_relation_verification'] = dependency_verification
# 4. 验证自指地位
self_ref_verification = self._verify_self_reference_status(level_verification['levels'])
results['self_reference_verification'] = self_ref_verification
# 5. 验证存在完备性
completeness_verification = self._verify_existence_completeness(level_verification['levels'])
results['completeness_verification'] = completeness_verification
# 6. 总体评估
results['overall_assessment'] = self._assess_verification_results(results)
return results
def _verify_ontological_levels(self, max_level: int) -> Dict[str, Any]:
"""验证本体论层级构造"""
verification = {
'levels': None,
'construction_success': False,
'consistency_verified': False,
'level_separation_verified': False,
'construction_rules_verified': False
}
try:
# 构造层级
levels = self.oss.create_ontological_levels(max_level)
verification['levels'] = levels
verification['construction_success'] = True
# 验证一致性
verification['consistency_verified'] = levels.get('consistency_verified', False)
# 验证层级分离
verification['level_separation_verified'] = self.oss._verify_level_separation(levels)
# 验证构造规则
verification['construction_rules_verified'] = self.oss._verify_construction_rules(levels)
except Exception as e:
verification['error'] = str(e)
return verification
def _verify_existence_proofs(self, levels: Dict[str, Any]) -> Dict[str, Any]:
"""验证存在证明"""
verification = {
'total_entities_tested': 0,
'proofs_found': 0,
'proof_success_rate': 0.0,
'constructive_proofs': 0,
'no11_compliant_proofs': 0,
'proof_details': []
}
if not levels:
return verification
# 测试每个层级的部分实体
for level_info in levels.get('levels', []):
entities_to_test = level_info['entities'][:2] # 限制测试数量
for entity in entities_to_test:
verification['total_entities_tested'] += 1
entity_id = entity['id']
try:
proof = self.oss.construct_existence_proof(entity_id, levels)
detail = {
'entity_id': entity_id,
'proof_found': proof.get('proof_found', False),
'proof_steps': len(proof.get('proof_steps', [])),
'dependencies_satisfied': proof.get('dependencies_satisfied', False),
'encoding_length': len(proof.get('proof_encoding', ''))
}
if proof.get('proof_found', False):
verification['proofs_found'] += 1
# 检查构造性
if proof.get('dependencies_satisfied', False):
verification['constructive_proofs'] += 1
# 检查no-11约束
encoding = proof.get('proof_encoding', '')
if encoding and '11' not in encoding:
verification['no11_compliant_proofs'] += 1
verification['proof_details'].append(detail)
except Exception as e:
verification['proof_details'].append({
'entity_id': entity_id,
'error': str(e)
})
# 计算成功率
if verification['total_entities_tested'] > 0:
verification['proof_success_rate'] = (
verification['proofs_found'] / verification['total_entities_tested']
)
return verification
def _verify_dependency_relations(self, levels: Dict[str, Any]) -> Dict[str, Any]:
"""验证依赖关系"""
verification = {
'dependency_analysis': {},
'transitivity_verified': False,
'acyclicity_verified': False,
'level_consistency_verified': False,
'hierarchy_theorem_verified': False
}
if not levels:
return verification
try:
# 运行依赖分析
dependency_analysis = self.oss.analyze_dependency_relations(levels)
verification['dependency_analysis'] = dependency_analysis
# 提取验证结果
verification['transitivity_verified'] = dependency_analysis.get('transitivity_verified', False)
verification['acyclicity_verified'] = dependency_analysis.get('acyclicity_verified', False)
verification['level_consistency_verified'] = dependency_analysis.get('level_consistency_verified', False)
# 验证层级定理
verification['hierarchy_theorem_verified'] = self._verify_hierarchy_theorem(levels)
except Exception as e:
verification['error'] = str(e)
return verification
def _verify_hierarchy_theorem(self, levels: Dict[str, Any]) -> bool:
"""验证依赖层级定理"""
# 验证：如果e1依赖于e2，则level(e2) <= level(e1)
for level_info in levels.get('levels', []):
level_num = level_info['level']
for entity in level_info['entities']:
dependencies = entity.get('construction_dependencies', [])
for dep in dependencies:
dep_level = self.oss._extract_entity_level(dep)
# 验证层级关系
if dep_level > level_num:
return False # 违反层级定理
return True
def _verify_self_reference_status(self, levels: Dict[str, Any]) -> Dict[str, Any]:
"""验证自指地位"""
verification = {
'self_reference_found': False,
'highest_level_verified': False,
'self_foundation_verified': False,
'complete_generation_verified': False,
'self_proof_verified': False
}
if not levels:
return verification
try:
# 运行自指验证
self_ref_results = self.oss.verify_self_reference_status(levels)
# 提取验证结果
verification['self_reference_found'] = self_ref_results.get('self_reference_entity') is not None
verification['highest_level_verified'] = self_ref_results.get('highest_level', 0) > 0
verification['self_foundation_verified'] = self_ref_results.get('self_foundation_verified', False)
verification['complete_generation_verified'] = self_ref_results.get('complete_generation_verified', False)
verification['self_proof_verified'] = self_ref_results.get('self_proof_verified', False)
except Exception as e:
verification['error'] = str(e)
return verification
def _verify_existence_completeness(self, levels: Dict[str, Any]) -> Dict[str, Any]:
"""验证存在完备性"""
verification = {
'completeness_check': {},
'decidability_verified': False,
'coverage_rate': 0.0,
'level_completeness_verified': False
}
if not levels:
return verification
try:
# 运行完备性检查
completeness_check = self.oss.check_existence_completeness(levels)
verification['completeness_check'] = completeness_check
# 提取验证结果
verification['decidability_verified'] = completeness_check.get('decidability_verified', False)
verification['coverage_rate'] = completeness_check.get('completeness_rate', 0.0)
# 验证层级完备性
level_completeness = completeness_check.get('level_completeness', {})
if level_completeness:
avg_level_completeness = sum(
lc.get('completeness_rate', 0) for lc in level_completeness.values()
) / len(level_completeness)
verification['level_completeness_verified'] = avg_level_completeness > 0.1
except Exception as e:
verification['error'] = str(e)
return verification
def _assess_verification_results(self, results: Dict[str, Any]) -> Dict[str, Any]:
"""评估验证结果"""
assessment = {
'ontological_levels_verified': False,
'existence_proofs_verified': False,
'dependency_relations_verified': False,
'self_reference_verified': False,
'completeness_verified': False,
'corollary_support': 'Weak'
}
# 评估本体论层级
level_verification = results.get('ontological_level_verification', {})
if (level_verification.get('construction_success', False) and
level_verification.get('consistency_verified', False) and
level_verification.get('level_separation_verified', False)):
assessment['ontological_levels_verified'] = True
# 评估存在证明
proof_verification = results.get('existence_proof_verification', {})
if proof_verification.get('proof_success_rate', 0) > 0.8:
assessment['existence_proofs_verified'] = True
# 评估依赖关系
dependency_verification = results.get('dependency_relation_verification', {})
if (dependency_verification.get('transitivity_verified', False) and
dependency_verification.get('acyclicity_verified', False) and
dependency_verification.get('level_consistency_verified', False)):
assessment['dependency_relations_verified'] = True
# 评估自指地位
self_ref_verification = results.get('self_reference_verification', {})
if (self_ref_verification.get('self_reference_found', False) and
self_ref_verification.get('highest_level_verified', False)):
assessment['self_reference_verified'] = True
# 评估完备性
completeness_verification = results.get('completeness_verification', {})
if (completeness_verification.get('decidability_verified', False) and
completeness_verification.get('coverage_rate', 0) > 0.05):
assessment['completeness_verified'] = True
# 综合评分
score = sum([
assessment['ontological_levels_verified'],
assessment['existence_proofs_verified'],
assessment['dependency_relations_verified'],
assessment['self_reference_verified'],
assessment['completeness_verified']
]) / 5.0
if score > 0.8:
assessment['corollary_support'] = 'Strong'
elif score > 0.6:
assessment['corollary_support'] = 'Moderate'
return assessment
2. 总结
本形式化框架提供了：
- 本体论地位系统：实现存在层级构造、存在证明和依赖关系分析
- 存在层级分析器：分析存在结构、复杂度和还原关系
- 本体论地位验证器：全面测试本体论地位推论的各个方面
这为C7-1本体论地位推论提供了严格的形式化基础和可验证的实现。