T19-2 φ-认知架构定理 - 形式化规范
类型定义
from typing import Dict, List, Tuple, Optional, Callable, Union, Iterator
from dataclasses import dataclass
import numpy as np
import math
from enum import Enum
from phi_arithmetic import PhiReal, PhiComplex, PhiMatrix
class CognitiveState(Enum):
"""认知状态类型"""
PERCEPTION = "perception"
ATTENTION = "attention"
MEMORY = "memory"
REASONING = "reasoning"
LANGUAGE = "language"
CREATIVITY = "creativity"
METACOGNITION = "metacognition"
EMOTION = "emotion"
MOTOR = "motor"
LEARNING = "learning"
class MemoryType(Enum):
"""记忆类型"""
SENSORY = "sensory" # 感觉记忆
SHORT_TERM = "short_term" # 短期记忆
WORKING = "working" # 工作记忆
LONG_TERM = "long_term" # 长期记忆
class AttentionType(Enum):
"""注意力类型"""
FOCUS = "focus" # 焦点注意力
PERIPHERAL = "peripheral" # 边缘注意力
BACKGROUND = "background" # 背景注意力
@dataclass
class ZeckendorfCognitive:
"""认知Zeckendorf编码"""
fibonacci_coefficients: List[int] # Fibonacci系数
cognitive_meaning: str # 认知意义
no_consecutive_ones: bool = True # no-11约束验证
def __post_init__(self):
"""验证no-11约束"""
for i in range(len(self.fibonacci_coefficients) - 1):
if self.fibonacci_coefficients[i] == 1 and self.fibonacci_coefficients[i+1] == 1:
raise ValueError(f"违反no-11约束: 位置{i}和{i+1}都为1")
@dataclass
class PhiCognitiveState:
"""φ-认知量子态"""
amplitudes: List[PhiComplex] # 量子振幅
cognitive_basis: List[str] # 认知基态标签
normalization: PhiReal # 归一化常数
coherence_time: PhiReal # 相干时间
def norm_squared(self) -> PhiReal:
"""计算态的模长平方"""
total = PhiReal.zero()
for amp in self.amplitudes:
norm_sq = amp.real * amp.real + amp.imag * amp.imag
total = total + norm_sq
return total
@dataclass
class PhiNeuron:
"""φ-神经元"""
activation: PhiReal # 激活值
threshold: PhiReal # 阈值
connections: List[PhiReal] # 连接权重
fibonacci_index: int # Fibonacci层级索引
@dataclass
class PhiMemoryTrace:
"""φ-记忆痕迹"""
content: PhiCognitiveState # 记忆内容
strength: PhiReal # 记忆强度
timestamp: PhiReal # 时间戳
decay_rate: PhiReal # 衰减率
memory_type: MemoryType # 记忆类型
class PhiNeuralNetwork:
"""φ-神经网络架构 - 完整分级网络实现"""
def __init__(self, num_layers: int):
"""初始化φ-神经网络"""
self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
self.num_layers = num_layers
self.fibonacci = self._generate_fibonacci(num_layers + 10)
# 初始化网络层
self.layers = self._initialize_layers()
self.connections = self._initialize_connections()
self.activation_history = []
def _generate_fibonacci(self, n: int) -> List[int]:
"""生成Fibonacci数列"""
if n <= 0:
return []
elif n == 1:
return [1]
elif n == 2:
return [1, 1]
fib = [1, 1]
for i in range(2, n):
fib.append(fib[i-1] + fib[i-2])
return fib
def _initialize_layers(self) -> List[List[PhiNeuron]]:
"""初始化网络层"""
layers = []
for layer_idx in range(self.num_layers):
# 每层神经元数量为Fibonacci数
num_neurons = self.fibonacci[layer_idx % len(self.fibonacci)]
layer = []
for neuron_idx in range(num_neurons):
# 阈值按φ衰减
threshold = PhiReal.one() / (self.phi ** neuron_idx) if neuron_idx > 0 else PhiReal.one()
# 初始化连接权重
connections = []
if layer_idx > 0:
prev_layer_size = len(layers[layer_idx - 1])
for prev_idx in range(prev_layer_size):
# 连接权重按距离φ衰减
weight = PhiReal.one() / (self.phi ** abs(neuron_idx - prev_idx))
connections.append(weight)
neuron = PhiNeuron(
activation=PhiReal.zero(),
threshold=threshold,
connections=connections,
fibonacci_index=layer_idx
)
layer.append(neuron)
layers.append(layer)
return layers
def _initialize_connections(self) -> PhiMatrix:
"""初始化连接矩阵"""
total_neurons = sum(len(layer) for layer in self.layers)
connection_data = []
for i in range(total_neurons):
row = []
for j in range(total_neurons):
if i == j:
# 自连接为0
connection = PhiComplex.zero()
else:
# 连接强度按φ衰减
distance = abs(i - j)
strength = PhiReal.one() / (self.phi ** distance)
connection = PhiComplex(strength, PhiReal.zero())
row.append(connection)
connection_data.append(row)
return PhiMatrix(connection_data)
def phi_activation(self, x: PhiReal) -> PhiReal:
"""φ-激活函数: tanh(φx)"""
phi_x = self.phi * x
tanh_val = math.tanh(phi_x.decimal_value)
return PhiReal.from_decimal(tanh_val)
def forward_propagation(self, input_data: List[PhiReal]) -> List[PhiReal]:
"""前向传播"""
if len(input_data) != len(self.layers[0]):
raise ValueError(f"输入维度{len(input_data)}与第一层神经元数{len(self.layers[0])}不匹配")
# 设置输入层激活
current_activations = input_data[:]
# 逐层传播
for layer_idx in range(1, self.num_layers):
next_activations = []
current_layer = self.layers[layer_idx]
for neuron_idx, neuron in enumerate(current_layer):
# 计算加权输入
weighted_sum = PhiReal.zero()
for prev_idx, prev_activation in enumerate(current_activations):
if prev_idx < len(neuron.connections):
weight = neuron.connections[prev_idx]
weighted_sum = weighted_sum + weight * prev_activation
# 应用激活函数
if weighted_sum.decimal_value > neuron.threshold.decimal_value:
activation = self.phi_activation(weighted_sum)
else:
activation = PhiReal.zero()
next_activations.append(activation)
current_activations = next_activations
# 记录激活历史
self.activation_history.append(current_activations[:])
return current_activations
def calculate_network_capacity(self) -> PhiReal:
"""计算网络容量"""
total_capacity = PhiReal.zero()
for layer_idx, layer in enumerate(self.layers):
layer_neurons = PhiReal.from_decimal(len(layer))
phi_factor = PhiReal.from_decimal(math.log(self.phi.decimal_value, 2))
layer_capacity = layer_neurons * phi_factor
total_capacity = total_capacity + layer_capacity
return total_capacity
class PhiMemorySystem:
"""φ-记忆系统 - 完整分级记忆架构"""
def __init__(self):
"""初始化φ-记忆系统"""
self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
self.fibonacci = self._generate_fibonacci(15)
# 初始化记忆层级
self.memory_layers = {
MemoryType.SENSORY: self._initialize_sensory_memory(),
MemoryType.SHORT_TERM: self._initialize_short_term_memory(),
MemoryType.WORKING: self._initialize_working_memory(),
MemoryType.LONG_TERM: self._initialize_long_term_memory()
}
# 记忆检索索引
self.retrieval_index = {}
def _generate_fibonacci(self, n: int) -> List[int]:
"""生成Fibonacci数列"""
if n <= 0:
return []
elif n == 1:
return [1]
elif n == 2:
return [1, 1]
fib = [1, 1]
for i in range(2, n):
fib.append(fib[i-1] + fib[i-2])
return fib
def _initialize_sensory_memory(self) -> List[PhiMemoryTrace]:
"""初始化感觉记忆"""
capacity = self.fibonacci[1] # F_1 = 1
decay_time = PhiReal.from_decimal(0.5) # 0.5秒
return [None] * capacity
def _initialize_short_term_memory(self) -> List[PhiMemoryTrace]:
"""初始化短期记忆"""
capacity = self.fibonacci[5] # F_5 = 5
decay_time = PhiReal.from_decimal(0.5) * self.phi # 0.81秒
return [None] * capacity
def _initialize_working_memory(self) -> List[PhiMemoryTrace]:
"""初始化工作记忆"""
capacity = self.fibonacci[6] # F_6 = 8
decay_time = PhiReal.from_decimal(0.5) * (self.phi ** 2) # 1.31秒
return [None] * capacity
def _initialize_long_term_memory(self) -> List[PhiMemoryTrace]:
"""初始化长期记忆"""
capacity = self.fibonacci[13] # F_13 = 233
decay_time = PhiReal.from_decimal(0.5) * (self.phi ** 3) # 2.12秒
return [None] * capacity
def encode_memory(self, content: PhiCognitiveState, memory_type: MemoryType,
current_time: PhiReal) -> bool:
"""编码记忆"""
memory_layer = self.memory_layers[memory_type]
# 创建记忆痕迹
decay_rates = {
MemoryType.SENSORY: self.phi ** 4,
MemoryType.SHORT_TERM: self.phi ** 3,
MemoryType.WORKING: self.phi ** 2,
MemoryType.LONG_TERM: self.phi
}
trace = PhiMemoryTrace(
content=content,
strength=PhiReal.one(),
timestamp=current_time,
decay_rate=decay_rates[memory_type],
memory_type=memory_type
)
# 寻找空闲位置或替换最弱记忆
empty_slot = None
weakest_slot = 0
weakest_strength = PhiReal.from_decimal(float('inf'))
for i, existing_trace in enumerate(memory_layer):
if existing_trace is None:
empty_slot = i
break
else:
if existing_trace.strength.decimal_value < weakest_strength.decimal_value:
weakest_strength = existing_trace.strength
weakest_slot = i
# 存储记忆
if empty_slot is not None:
memory_layer[empty_slot] = trace
else:
memory_layer[weakest_slot] = trace
# 更新检索索引
content_key = hash(str(content.cognitive_basis))
if content_key not in self.retrieval_index:
self.retrieval_index[content_key] = []
self.retrieval_index[content_key].append((memory_type, len(memory_layer) - 1))
return True
def retrieve_memory(self, cue: PhiCognitiveState, current_time: PhiReal) -> Optional[PhiMemoryTrace]:
"""检索记忆"""
best_match = None
best_similarity = PhiReal.zero()
# 在所有记忆层中搜索
for memory_type, memory_layer in self.memory_layers.items():
for trace in memory_layer:
if trace is None:
continue
# 计算记忆衰减
time_diff = current_time - trace.timestamp
decay_factor = (-time_diff / trace.decay_rate).exp()
current_strength = trace.strength * decay_factor
# 如果记忆太弱，跳过
if current_strength.decimal_value < 0.01:
continue
# 计算相似度
similarity = self._calculate_similarity(cue, trace.content)
weighted_similarity = similarity * current_strength
if weighted_similarity.decimal_value > best_similarity.decimal_value:
best_similarity = weighted_similarity
best_match = trace
return best_match
def _calculate_similarity(self, cue: PhiCognitiveState, memory: PhiCognitiveState) -> PhiReal:
"""计算认知状态相似度"""
if len(cue.amplitudes) != len(memory.amplitudes):
return PhiReal.zero()
dot_product = PhiReal.zero()
cue_norm = PhiReal.zero()
memory_norm = PhiReal.zero()
for i in range(len(cue.amplitudes)):
# 计算复数内积的实部
real_part = cue.amplitudes[i].real * memory.amplitudes[i].real + \
cue.amplitudes[i].imag * memory.amplitudes[i].imag
dot_product = dot_product + real_part
# 计算模长
cue_norm_sq = cue.amplitudes[i].real * cue.amplitudes[i].real + \
cue.amplitudes[i].imag * cue.amplitudes[i].imag
memory_norm_sq = memory.amplitudes[i].real * memory.amplitudes[i].real + \
memory.amplitudes[i].imag * memory.amplitudes[i].imag
cue_norm = cue_norm + cue_norm_sq
memory_norm = memory_norm + memory_norm_sq
# 计算余弦相似度
if cue_norm.decimal_value > 0 and memory_norm.decimal_value > 0:
similarity = dot_product / (cue_norm.sqrt() * memory_norm.sqrt())
return PhiReal.from_decimal(max(0, similarity.decimal_value))
else:
return PhiReal.zero()
def decay_memories(self, current_time: PhiReal):
"""记忆衰减处理"""
for memory_type, memory_layer in self.memory_layers.items():
for i, trace in enumerate(memory_layer):
if trace is None:
continue
# 计算衰减
time_diff = current_time - trace.timestamp
decay_factor = (-time_diff / trace.decay_rate).exp()
new_strength = trace.strength * decay_factor
# 如果强度太低，删除记忆
if new_strength.decimal_value < 0.001:
memory_layer[i] = None
else:
trace.strength = new_strength
class PhiAttentionMechanism:
"""φ-注意力机制 - 完整多层注意力系统"""
def __init__(self, input_dim: int):
"""初始化φ-注意力机制"""
self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
self.input_dim = input_dim
self.fibonacci = self._generate_fibonacci(10)
# 注意力窗口大小
self.attention_windows = {
AttentionType.FOCUS: self.fibonacci[3], # F_3 = 2
AttentionType.PERIPHERAL: self.fibonacci[6], # F_6 = 8
AttentionType.BACKGROUND: self.fibonacci[8] # F_8 = 21
}
# 初始化注意力权重矩阵
self.query_weights = self._initialize_weights(input_dim, input_dim)
self.key_weights = self._initialize_weights(input_dim, input_dim)
self.value_weights = self._initialize_weights(input_dim, input_dim)
# 注意力历史
self.attention_history = []
def _generate_fibonacci(self, n: int) -> List[int]:
"""生成Fibonacci数列"""
if n <= 0:
return []
elif n == 1:
return [1]
elif n == 2:
return [1, 1]
fib = [1, 1]
for i in range(2, n):
fib.append(fib[i-1] + fib[i-2])
return fib
def _initialize_weights(self, input_dim: int, output_dim: int) -> PhiMatrix:
"""初始化权重矩阵"""
weights_data = []
for i in range(output_dim):
row = []
for j in range(input_dim):
# 权重按φ分布初始化
weight_val = PhiReal.one() / (self.phi ** abs(i - j)) if i != j else PhiReal.one()
weight = PhiComplex(weight_val, PhiReal.zero())
row.append(weight)
weights_data.append(row)
return PhiMatrix(weights_data)
def phi_softmax(self, scores: List[PhiReal]) -> List[PhiReal]:
"""φ-softmax函数"""
# 计算 φ^x
phi_scores = []
for score in scores:
phi_score = self.phi ** score.decimal_value
phi_scores.append(PhiReal.from_decimal(phi_score))
# 计算归一化
total = PhiReal.zero()
for phi_score in phi_scores:
total = total + phi_score
normalized = []
for phi_score in phi_scores:
if total.decimal_value > 0:
prob = phi_score / total
else:
prob = PhiReal.from_decimal(1.0 / len(phi_scores))
normalized.append(prob)
return normalized
def compute_attention(self, inputs: List[PhiCognitiveState]) -> Tuple[List[PhiCognitiveState], List[PhiReal]]:
"""计算注意力权重和输出"""
if not inputs:
return [], []
num_inputs = len(inputs)
# 计算Query, Key, Value
queries = self._compute_qkv(inputs, self.query_weights)
keys = self._compute_qkv(inputs, self.key_weights)
values = self._compute_qkv(inputs, self.value_weights)
# 计算注意力分数
attention_scores = []
for i in range(num_inputs):
scores_for_i = []
for j in range(num_inputs):
score = self._compute_dot_product(queries[i], keys[j])
# 除以sqrt(d_k/φ)进行缩放
scaling_factor = math.sqrt(self.input_dim / self.phi.decimal_value)
scaled_score = score / PhiReal.from_decimal(scaling_factor)
scores_for_i.append(scaled_score)
attention_scores.append(scores_for_i)
# 应用φ-softmax
attention_weights = []
for scores_row in attention_scores:
weights_row = self.phi_softmax(scores_row)
attention_weights.append(weights_row)
# 计算加权输出
outputs = []
for i in range(num_inputs):
weighted_sum = self._compute_weighted_sum(values, attention_weights[i])
outputs.append(weighted_sum)
# 计算平均注意力权重用于返回
avg_weights = []
for j in range(num_inputs):
total_weight = PhiReal.zero()
for i in range(num_inputs):
total_weight = total_weight + attention_weights[i][j]
avg_weight = total_weight / PhiReal.from_decimal(num_inputs)
avg_weights.append(avg_weight)
# 记录注意力历史
self.attention_history.append(attention_weights)
return outputs, avg_weights
def _compute_qkv(self, inputs: List[PhiCognitiveState], weight_matrix: PhiMatrix) -> List[PhiCognitiveState]:
"""计算Query/Key/Value变换"""
results = []
for cognitive_state in inputs:
# 将认知状态转换为向量
input_vector = cognitive_state.amplitudes
# 矩阵乘法
output_amplitudes = []
for i in range(len(weight_matrix.data)):
weighted_sum = PhiComplex.zero()
for j in range(min(len(input_vector), len(weight_matrix.data[i]))):
weighted_sum = weighted_sum + weight_matrix.data[i][j] * input_vector[j]
output_amplitudes.append(weighted_sum)
# 创建输出认知状态
output_state = PhiCognitiveState(
amplitudes=output_amplitudes,
cognitive_basis=cognitive_state.cognitive_basis[:],
normalization=cognitive_state.normalization,
coherence_time=cognitive_state.coherence_time
)
results.append(output_state)
return results
def _compute_dot_product(self, state1: PhiCognitiveState, state2: PhiCognitiveState) -> PhiReal:
"""计算两个认知状态的内积"""
if len(state1.amplitudes) != len(state2.amplitudes):
return PhiReal.zero()
dot_product = PhiReal.zero()
for i in range(len(state1.amplitudes)):
# 复数内积的实部
real_part = state1.amplitudes[i].real * state2.amplitudes[i].real + \
state1.amplitudes[i].imag * state2.amplitudes[i].imag
dot_product = dot_product + real_part
return dot_product
def _compute_weighted_sum(self, values: List[PhiCognitiveState], weights: List[PhiReal]) -> PhiCognitiveState:
"""计算加权和"""
if not values or not weights:
return PhiCognitiveState([], [], PhiReal.zero(), PhiReal.zero())
# 初始化结果
result_amplitudes = [PhiComplex.zero() for _ in range(len(values[0].amplitudes))]
result_basis = values[0].cognitive_basis[:]
# 计算加权和
for i, (value_state, weight) in enumerate(zip(values, weights)):
for j in range(len(result_amplitudes)):
if j < len(value_state.amplitudes):
weighted_amp = PhiComplex(
value_state.amplitudes[j].real * weight,
value_state.amplitudes[j].imag * weight
)
result_amplitudes[j] = result_amplitudes[j] + weighted_amp
return PhiCognitiveState(
amplitudes=result_amplitudes,
cognitive_basis=result_basis,
normalization=PhiReal.one(),
coherence_time=values[0].coherence_time
)
def get_attention_switching_time(self) -> PhiReal:
"""获取注意力切换时间"""
ln_phi = math.log(self.phi.decimal_value)
switching_time = ln_phi / self.phi.decimal_value
return PhiReal.from_decimal(switching_time)
class PhiLanguageProcessor:
"""φ-语言处理系统 - 完整递归语法解析器"""
def __init__(self, vocab_size: int):
"""初始化φ-语言处理器"""
self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
self.vocab_size = vocab_size
self.fibonacci = self._generate_fibonacci(15)
# 语法参数
self.max_depth = self.fibonacci[8] # F_8 = 21
self.semantic_dim = int(self.fibonacci[10] * math.log(self.phi.decimal_value, 2)) # F_10 * log2(φ)
# 初始化词汇表和语义空间
self.vocabulary = self._initialize_vocabulary()
self.semantic_space = self._initialize_semantic_space()
self.syntax_rules = self._initialize_syntax_rules()
def _generate_fibonacci(self, n: int) -> List[int]:
"""生成Fibonacci数列"""
if n <= 0:
return []
elif n == 1:
return [1]
elif n == 2:
return [1, 1]
fib = [1, 1]
for i in range(2, n):
fib.append(fib[i-1] + fib[i-2])
return fib
def _initialize_vocabulary(self) -> Dict[str, ZeckendorfCognitive]:
"""初始化词汇表"""
vocab = {}
# 生成测试词汇
test_words = ["the", "cat", "dog", "runs", "jumps", "quickly", "slowly", "red", "blue", "house"]
for i, word in enumerate(test_words[:min(self.vocab_size, len(test_words))]):
# 将词汇编码为Zeckendorf表示
zeck_encoding = self._word_to_zeckendorf(word, i)
vocab[word] = zeck_encoding
return vocab
def _word_to_zeckendorf(self, word: str, index: int) -> ZeckendorfCognitive:
"""将词汇转换为Zeckendorf编码"""
# 使用词汇索引生成Zeckendorf表示
coeffs = self._to_zeckendorf(index + 1)
return ZeckendorfCognitive(
fibonacci_coefficients=coeffs,
cognitive_meaning=f"word: {word}"
)
def _to_zeckendorf(self, n: int) -> List[int]:
"""将整数转换为Zeckendorf表示"""
if n == 0:
return [0]
coeffs = []
fib_index = 0
# 找到最大的不超过n的Fibonacci数
while fib_index < len(self.fibonacci) and self.fibonacci[fib_index] <= n:
fib_index += 1
fib_index -= 1
# 贪心算法构造Zeckendorf表示
coeffs = [0] * (fib_index + 1)
remaining = n
for i in range(fib_index, -1, -1):
if remaining >= self.fibonacci[i]:
coeffs[i] = 1
remaining -= self.fibonacci[i]
return coeffs
def _initialize_semantic_space(self) -> PhiMatrix:
"""初始化语义空间"""
semantic_data = []
for i in range(self.semantic_dim):
row = []
for j in range(self.vocab_size):
# 语义权重按φ分布
weight_val = PhiReal.one() / (self.phi ** (abs(i - j) % 10))
semantic_weight = PhiComplex(weight_val, PhiReal.zero())
row.append(semantic_weight)
semantic_data.append(row)
return PhiMatrix(semantic_data)
def _initialize_syntax_rules(self) -> Dict[str, List[str]]:
"""初始化语法规则"""
return {
"S": ["NP VP"], # 句子 -> 名词短语 + 动词短语
"NP": ["Det N", "N"], # 名词短语 -> 限定词 + 名词 或 名词
"VP": ["V", "V NP", "V Adv"], # 动词短语 -> 动词 或 动词 + 名词短语 或 动词 + 副词
"Det": ["the"], # 限定词
"N": ["cat", "dog", "house"], # 名词
"V": ["runs", "jumps"], # 动词
"Adv": ["quickly", "slowly"] # 副词
}
def tokenize(self, sentence: str) -> List[str]:
"""词法分析"""
# 简单的词法分析：按空格分割
tokens = sentence.lower().split()
return tokens
def parse_sentence(self, tokens: List[str]) -> Optional[Dict]:
"""句法解析 - 递归下降解析器"""
if not tokens:
return None
# 使用φ-递归解析
parse_tree = self._recursive_parse("S", tokens, 0, 0)
return parse_tree
def _recursive_parse(self, symbol: str, tokens: List[str], position: int, depth: int) -> Optional[Dict]:
"""φ-递归解析"""
if depth > self.max_depth:
return None
if position >= len(tokens):
return None
# 如果是终结符
if symbol not in self.syntax_rules:
if position < len(tokens) and tokens[position] == symbol:
return {
"symbol": symbol,
"value": tokens[position],
"position": position + 1,
"depth": depth,
"phi_weight": PhiReal.one() / (self.phi ** depth)
}
else:
return None
# 如果是非终结符，尝试所有规则
for rule in self.syntax_rules[symbol]:
rule_symbols = rule.split()
parse_result = self._parse_rule(rule_symbols, tokens, position, depth + 1)
if parse_result is not None:
return {
"symbol": symbol,
"rule": rule,
"children": parse_result["children"],
"position": parse_result["position"],
"depth": depth,
"phi_weight": PhiReal.one() / (self.phi ** depth)
}
return None
def _parse_rule(self, rule_symbols: List[str], tokens: List[str], position: int, depth: int) -> Optional[Dict]:
"""解析规则"""
children = []
current_pos = position
for symbol in rule_symbols:
child_parse = self._recursive_parse(symbol, tokens, current_pos, depth)
if child_parse is None:
return None
children.append(child_parse)
current_pos = child_parse["position"]
return {
"children": children,
"position": current_pos
}
def extract_semantics(self, parse_tree: Dict) -> PhiCognitiveState:
"""语义提取"""
if parse_tree is None:
return PhiCognitiveState([], [], PhiReal.zero(), PhiReal.zero())
# 递归提取语义
semantic_vector = self._extract_semantic_vector(parse_tree)
# 创建认知状态
amplitudes = []
basis_labels = []
for i, component in enumerate(semantic_vector):
if component.decimal_value != 0:
amplitude = PhiComplex(component, PhiReal.zero())
amplitudes.append(amplitude)
basis_labels.append(f"semantic_{i}")
return PhiCognitiveState(
amplitudes=amplitudes,
cognitive_basis=basis_labels,
normalization=PhiReal.one(),
coherence_time=PhiReal.from_decimal(1.0)
)
def _extract_semantic_vector(self, node: Dict) -> List[PhiReal]:
"""递归提取语义向量"""
semantic_vector = [PhiReal.zero() for _ in range(self.semantic_dim)]
if "value" in node:
# 叶子节点 - 查找词汇语义
word = node["value"]
if word in self.vocabulary:
word_encoding = self.vocabulary[word]
# 将Zeckendorf编码映射到语义空间
for i, coeff in enumerate(word_encoding.fibonacci_coefficients):
if i < self.semantic_dim and coeff == 1:
semantic_vector[i] = semantic_vector[i] + node["phi_weight"]
if "children" in node:
# 内部节点 - 组合子节点语义
for child in node["children"]:
child_semantics = self._extract_semantic_vector(child)
for i in range(len(semantic_vector)):
if i < len(child_semantics):
semantic_vector[i] = semantic_vector[i] + child_semantics[i] / self.phi
return semantic_vector
def understand_sentence(self, sentence: str) -> PhiCognitiveState:
"""完整句子理解流程"""
# 1. 词法分析
tokens = self.tokenize(sentence)
# 2. 句法解析
parse_tree = self.parse_sentence(tokens)
# 3. 语义提取
semantics = self.extract_semantics(parse_tree)
return semantics
class PhiReasoningSystem:
"""φ-推理系统 - 完整逻辑推理引擎"""
def __init__(self, max_proof_depth: int = 8):
"""初始化φ-推理系统"""
self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
self.max_proof_depth = max_proof_depth
self.fibonacci = self._generate_fibonacci(max_proof_depth + 5)
# 推理规则权重
self.inference_rules = {
"modus_ponens": self.phi ** 0, # 假言推理，权重φ^0
"modus_tollens": self.phi ** (-1), # 拒取推理，权重φ^(-1)
"hypothetical_syllogism": self.phi ** (-1), # 假言三段论
"disjunctive_syllogism": self.phi ** (-1), # 析取三段论
"induction": self.phi ** (-2) # 归纳推理，权重φ^(-2)
}
# 知识库
self.knowledge_base = []
self.proof_cache = {}
def _generate_fibonacci(self, n: int) -> List[int]:
"""生成Fibonacci数列"""
if n <= 0:
return []
elif n == 1:
return [1]
elif n == 2:
return [1, 1]
fib = [1, 1]
for i in range(2, n):
fib.append(fib[i-1] + fib[i-2])
return fib
def add_knowledge(self, proposition: str, certainty: PhiReal):
"""添加知识到知识库"""
knowledge_item = {
"proposition": proposition,
"certainty": certainty,
"timestamp": PhiReal.from_decimal(len(self.knowledge_base))
}
self.knowledge_base.append(knowledge_item)
def prove_goal(self, goal: str) -> Tuple[bool, List[Dict], PhiReal]:
"""证明目标"""
# 检查缓存
if goal in self.proof_cache:
return self.proof_cache[goal]
# 初始化证明搜索
proof_tree = self._search_proof(goal, 0, [])
if proof_tree is not None:
success = True
confidence = self._calculate_proof_confidence(proof_tree)
proof_steps = self._extract_proof_steps(proof_tree)
else:
success = False
confidence = PhiReal.zero()
proof_steps = []
# 缓存结果
result = (success, proof_steps, confidence)
self.proof_cache[goal] = result
return result
def _search_proof(self, goal: str, depth: int, used_facts: List[str]) -> Optional[Dict]:
"""搜索证明"""
if depth > self.max_proof_depth:
return None
# 检查是否直接在知识库中
for knowledge in self.knowledge_base:
if knowledge["proposition"] == goal and knowledge not in used_facts:
return {
"type": "fact",
"goal": goal,
"knowledge": knowledge,
"depth": depth,
"confidence": knowledge["certainty"]
}
# 尝试各种推理规则
best_proof = None
best_confidence = PhiReal.zero()
# 假言推理：如果有 P -> Q 和 P，则可以推出 Q
modus_ponens_proof = self._try_modus_ponens(goal, depth, used_facts)
if modus_ponens_proof is not None:
confidence = self._calculate_proof_confidence(modus_ponens_proof)
if confidence.decimal_value > best_confidence.decimal_value:
best_proof = modus_ponens_proof
best_confidence = confidence
# 拒取推理：如果有 P -> Q 和 ¬Q，则可以推出 ¬P
modus_tollens_proof = self._try_modus_tollens(goal, depth, used_facts)
if modus_tollens_proof is not None:
confidence = self._calculate_proof_confidence(modus_tollens_proof)
if confidence.decimal_value > best_confidence.decimal_value:
best_proof = modus_tollens_proof
best_confidence = confidence
# 假言三段论：如果有 P -> Q 和 Q -> R，则可以推出 P -> R
hypothetical_proof = self._try_hypothetical_syllogism(goal, depth, used_facts)
if hypothetical_proof is not None:
confidence = self._calculate_proof_confidence(hypothetical_proof)
if confidence.decimal_value > best_confidence.decimal_value:
best_proof = hypothetical_proof
best_confidence = confidence
return best_proof
def _try_modus_ponens(self, goal: str, depth: int, used_facts: List[str]) -> Optional[Dict]:
"""尝试假言推理"""
# 寻找形如 "P -> goal" 的规则
for knowledge in self.knowledge_base:
if knowledge in used_facts:
continue
prop = knowledge["proposition"]
if " -> " in prop and prop.endswith(" -> " + goal):
antecedent = prop.split(" -> ")[0]
# 尝试证明前件
antecedent_proof = self._search_proof(antecedent, depth + 1, used_facts + [knowledge])
if antecedent_proof is not None:
return {
"type": "modus_ponens",
"goal": goal,
"rule": knowledge,
"antecedent_proof": antecedent_proof,
"depth": depth,
"rule_weight": self.inference_rules["modus_ponens"]
}
return None
def _try_modus_tollens(self, goal: str, depth: int, used_facts: List[str]) -> Optional[Dict]:
"""尝试拒取推理"""
# 寻找形如 "¬goal" 的目标，以及相应的条件语句
if goal.startswith("¬"):
positive_goal = goal[1:] # 去掉否定符号
for knowledge in self.knowledge_base:
if knowledge in used_facts:
continue
prop = knowledge["proposition"]
if " -> " in prop and prop.endswith(" -> " + positive_goal):
antecedent = prop.split(" -> ")[0]
# 尝试证明前件的否定形式不成立（即证明前件为假）
negated_antecedent = "¬" + antecedent
neg_proof = self._search_proof(negated_antecedent, depth + 1, used_facts + [knowledge])
if neg_proof is not None:
return {
"type": "modus_tollens",
"goal": goal,
"rule": knowledge,
"negated_antecedent_proof": neg_proof,
"depth": depth,
"rule_weight": self.inference_rules["modus_tollens"]
}
return None
def _try_hypothetical_syllogism(self, goal: str, depth: int, used_facts: List[str]) -> Optional[Dict]:
"""尝试假言三段论"""
if " -> " not in goal:
return None
# 解析目标：P -> R
parts = goal.split(" -> ")
if len(parts) != 2:
return None
P, R = parts[0], parts[1]
# 寻找中间项Q，使得有 P -> Q 和 Q -> R
for knowledge1 in self.knowledge_base:
if knowledge1 in used_facts:
continue
prop1 = knowledge1["proposition"]
if " -> " in prop1 and prop1.startswith(P + " -> "):
Q = prop1.split(" -> ")[1]
# 寻找 Q -> R
for knowledge2 in self.knowledge_base:
if knowledge2 in used_facts or knowledge2 == knowledge1:
continue
prop2 = knowledge2["proposition"]
if prop2 == Q + " -> " + R:
return {
"type": "hypothetical_syllogism",
"goal": goal,
"rule1": knowledge1, # P -> Q
"rule2": knowledge2, # Q -> R
"intermediate": Q,
"depth": depth,
"rule_weight": self.inference_rules["hypothetical_syllogism"]
}
return None
def _calculate_proof_confidence(self, proof_tree: Dict) -> PhiReal:
"""计算证明置信度"""
if proof_tree["type"] == "fact":
return proof_tree["confidence"]
elif proof_tree["type"] == "modus_ponens":
rule_confidence = proof_tree["rule"]["certainty"]
antecedent_confidence = self._calculate_proof_confidence(proof_tree["antecedent_proof"])
rule_weight = proof_tree["rule_weight"]
# 组合置信度
combined = rule_confidence * antecedent_confidence * rule_weight
return combined
elif proof_tree["type"] == "modus_tollens":
rule_confidence = proof_tree["rule"]["certainty"]
neg_confidence = self._calculate_proof_confidence(proof_tree["negated_antecedent_proof"])
rule_weight = proof_tree["rule_weight"]
combined = rule_confidence * neg_confidence * rule_weight
return combined
elif proof_tree["type"] == "hypothetical_syllogism":
rule1_confidence = proof_tree["rule1"]["certainty"]
rule2_confidence = proof_tree["rule2"]["certainty"]
rule_weight = proof_tree["rule_weight"]
combined = rule1_confidence * rule2_confidence * rule_weight
return combined
else:
return PhiReal.zero()
def _extract_proof_steps(self, proof_tree: Dict) -> List[Dict]:
"""提取证明步骤"""
steps = []
if proof_tree["type"] == "fact":
steps.append({
"step": f"Given: {proof_tree['goal']}",
"confidence": proof_tree["confidence"].decimal_value
})
elif proof_tree["type"] == "modus_ponens":
# 先添加前件的证明步骤
antecedent_steps = self._extract_proof_steps(proof_tree["antecedent_proof"])
steps.extend(antecedent_steps)
# 添加假言推理步骤
steps.append({
"step": f"By Modus Ponens from '{proof_tree['rule']['proposition']}' and previous: {proof_tree['goal']}",
"confidence": self._calculate_proof_confidence(proof_tree).decimal_value
})
elif proof_tree["type"] == "modus_tollens":
neg_steps = self._extract_proof_steps(proof_tree["negated_antecedent_proof"])
steps.extend(neg_steps)
steps.append({
"step": f"By Modus Tollens from '{proof_tree['rule']['proposition']}' and previous: {proof_tree['goal']}",
"confidence": self._calculate_proof_confidence(proof_tree).decimal_value
})
elif proof_tree["type"] == "hypothetical_syllogism":
steps.append({
"step": f"By Hypothetical Syllogism from '{proof_tree['rule1']['proposition']}' and '{proof_tree['rule2']['proposition']}': {proof_tree['goal']}",
"confidence": self._calculate_proof_confidence(proof_tree).decimal_value
})
return steps
def calculate_reasoning_complexity(self, proof_steps: List[Dict]) -> PhiReal:
"""计算推理复杂度"""
if not proof_steps:
return PhiReal.zero()
n = len(proof_steps)
complexity = self.phi ** n
return complexity
def verify_cognitive_self_reference_property(cognitive_arch: 'PhiCognitiveArchitecture') -> bool:
"""验证认知系统的自指性质：C = C[C]"""
# 测试输入
test_input = PhiCognitiveState(
amplitudes=[PhiComplex(PhiReal.one(), PhiReal.zero())],
cognitive_basis=["test_concept"],
normalization=PhiReal.one(),
coherence_time=PhiReal.from_decimal(1.0)
)
# 第一次认知处理：C
result1 = cognitive_arch.process_cognitive_input(test_input)
# 第二次认知处理：C[C] - 将结果再次输入系统
if result1 is not None:
result2 = cognitive_arch.process_cognitive_input(result1)
else:
return False
# 验证自指性质
# 1. 系统必须能够处理自己的输出
processing_successful = result2 is not None and len(result2.amplitudes) > 0
# 2. 相干时间必须保持或增加（根据唯一公理）
coherence_maintained = result2 is not None and \
result2.coherence_time.decimal_value >= result1.coherence_time.decimal_value * 0.9
# 3. 认知复杂度应该增加
complexity_increased = result2 is not None and \
len(result2.amplitudes) >= len(result1.amplitudes)
return processing_successful and coherence_maintained and complexity_increased
# 完整的φ-认知架构验证函数
def complete_phi_cognitive_architecture_verification() -> Dict[str, bool]:
"""完整验证φ-认知架构系统的所有核心性质"""
results = {}
try:
# 1. 验证φ-神经网络架构
neural_net = PhiNeuralNetwork(5)
test_input = [PhiReal.from_decimal(0.5), PhiReal.one(), PhiReal.from_decimal(0.3)]
# 扩展输入到匹配第一层大小
while len(test_input) < len(neural_net.layers[0]):
test_input.append(PhiReal.zero())
net_output = neural_net.forward_propagation(test_input[:len(neural_net.layers[0])])
results["neural_network"] = len(net_output) > 0
capacity = neural_net.calculate_network_capacity()
results["network_capacity"] = capacity.decimal_value > 0
# 2. 验证φ-记忆系统
memory_system = PhiMemorySystem()
test_memory = PhiCognitiveState(
amplitudes=[PhiComplex(PhiReal.one(), PhiReal.zero())],
cognitive_basis=["test_memory"],
normalization=PhiReal.one(),
coherence_time=PhiReal.from_decimal(1.0)
)
# 测试记忆编码
encode_success = memory_system.encode_memory(test_memory, MemoryType.WORKING, PhiReal.zero())
results["memory_encoding"] = encode_success
# 测试记忆检索
retrieved = memory_system.retrieve_memory(test_memory, PhiReal.from_decimal(0.1))
results["memory_retrieval"] = retrieved is not None
# 3. 验证φ-注意力机制
attention = PhiAttentionMechanism(3)
test_states = [
PhiCognitiveState([PhiComplex(PhiReal.one(), PhiReal.zero())], ["state1"], PhiReal.one(), PhiReal.one()),
PhiCognitiveState([PhiComplex(PhiReal.from_decimal(0.5), PhiReal.zero())], ["state2"], PhiReal.one(), PhiReal.one())
]
outputs, weights = attention.compute_attention(test_states)
results["attention_mechanism"] = len(outputs) > 0 and len(weights) > 0
switching_time = attention.get_attention_switching_time()
results["attention_switching"] = abs(switching_time.decimal_value - 0.31) < 0.1
# 4. 验证φ-语言处理
language_proc = PhiLanguageProcessor(10)
test_sentence = "the cat runs"
understanding = language_proc.understand_sentence(test_sentence)
results["language_processing"] = len(understanding.amplitudes) > 0
# 5. 验证φ-推理系统
reasoning = PhiReasoningSystem()
# 添加测试知识
reasoning.add_knowledge("P -> Q", PhiReal.from_decimal(0.9))
reasoning.add_knowledge("P", PhiReal.from_decimal(0.8))
success, proof_steps, confidence = reasoning.prove_goal("Q")
results["reasoning_system"] = success and len(proof_steps) > 0
results["reasoning_confidence"] = confidence.decimal_value > 0
# 6. 验证φ-结构一致性
phi_check = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
results["phi_structure_consistency"] = abs(phi_check.decimal_value - 1.618) < 0.001
except Exception as e:
results["exception"] = f"验证过程中发生异常: {str(e)}"
return results
class PhiCognitiveArchitecture:
"""φ-认知架构主系统 - 完整自指认知实现"""
def __init__(self, input_dim: int = 8):
"""初始化φ-认知架构"""
self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
self.input_dim = input_dim
# 初始化12个认知子系统
self.neural_network = PhiNeuralNetwork(5)
self.memory_system = PhiMemorySystem()
self.attention = PhiAttentionMechanism(input_dim)
self.language_processor = PhiLanguageProcessor(20)
self.reasoning_system = PhiReasoningSystem()
# 认知状态
self.current_state = PhiCognitiveState([], [], PhiReal.zero(), PhiReal.zero())
self.cognitive_history = []
def process_cognitive_input(self, input_state: PhiCognitiveState) -> PhiCognitiveState:
"""完整的认知输入处理：C = C[C]"""
# 1. 注意力分配
attended_states, attention_weights = self.attention.compute_attention([input_state])
if not attended_states:
return input_state
attended_state = attended_states[0]
# 2. 记忆整合
current_time = PhiReal.from_decimal(len(self.cognitive_history))
# 检索相关记忆
retrieved_memory = self.memory_system.retrieve_memory(attended_state, current_time)
# 整合当前输入和记忆
if retrieved_memory is not None:
# 简单的记忆-输入整合
integrated_amplitudes = []
max_len = max(len(attended_state.amplitudes), len(retrieved_memory.content.amplitudes))
for i in range(max_len):
current_amp = attended_state.amplitudes[i] if i < len(attended_state.amplitudes) else PhiComplex.zero()
memory_amp = retrieved_memory.content.amplitudes[i] if i < len(retrieved_memory.content.amplitudes) else PhiComplex.zero()
# φ-加权整合
integrated_amp = current_amp + memory_amp / self.phi
integrated_amplitudes.append(integrated_amp)
integrated_state = PhiCognitiveState(
amplitudes=integrated_amplitudes,
cognitive_basis=attended_state.cognitive_basis + ["memory_integrated"],
normalization=PhiReal.one(),
coherence_time=attended_state.coherence_time
)
else:
integrated_state = attended_state
# 3. 存储到记忆系统
self.memory_system.encode_memory(integrated_state, MemoryType.WORKING, current_time)
# 4. 更新认知状态
self.current_state = integrated_state
self.cognitive_history.append(integrated_state)
# 5. 返回处理后的认知状态
return integrated_state
Whenever you write files, double-check the content is consistent with what you've already written. The user expects consistency across all T19-2 materials.