CS50 人工智能导论 Python - 知识
CS50's Introduction to Artificial Intelligence with Python - Knowledge
我正在学习哈佛的 Python 人工智能概论课程。我很享受。但是我下载了逻辑文件以使用布尔代数和知识，即简单的操作（或，与，非...）在我表示怀疑之前，我将分享来自哈佛源代码的知识class，我希望没有'关于它的问题：
link 到这个 class:
logic.py
import itertools
class Sentence():
def evaluate(self, model):
"""Evaluates the logical sentence."""
raise Exception("nothing to evaluate")
def formula(self):
"""Returns string formula representing logical sentence."""
return ""
def symbols(self):
"""Returns a set of all symbols in the logical sentence."""
return set()
@classmethod
def validate(cls, sentence):
if not isinstance(sentence, Sentence):
raise TypeError("must be a logical sentence")
@classmethod
def parenthesize(cls, s):
"""Parenthesizes an expression if not already parenthesized."""
def balanced(s):
"""Checks if a string has balanced parentheses."""
count = 0
for c in s:
if c == "(":
count += 1
elif c == ")":
if count <= 0:
return False
count -= 1
return count == 0
if not len(s) or s.isalpha() or (
s[0] == "(" and s[-1] == ")" and balanced(s[1:-1])
):
return s
else:
return f"({s})"
class Symbol(Sentence):
def __init__(self, name):
self.name = name
def __eq__(self, other):
return isinstance(other, Symbol) and self.name == other.name
def __hash__(self):
return hash(("symbol", self.name))
def __repr__(self):
return self.name
def evaluate(self, model):
try:
return bool(model[self.name])
except KeyError:
raise Exception(f"variable {self.name} not in model")
def formula(self):
return self.name
def symbols(self):
return {self.name}
class Not(Sentence):
def __init__(self, operand):
Sentence.validate(operand)
self.operand = operand
def __eq__(self, other):
return isinstance(other, Not) and self.operand == other.operand
def __hash__(self):
return hash(("not", hash(self.operand)))
def __repr__(self):
return f"Not({self.operand})"
def evaluate(self, model):
return not self.operand.evaluate(model)
def formula(self):
return "¬" + Sentence.parenthesize(self.operand.formula())
def symbols(self):
return self.operand.symbols()
class And(Sentence):
def __init__(self, *conjuncts):
for conjunct in conjuncts:
Sentence.validate(conjunct)
self.conjuncts = list(conjuncts)
def __eq__(self, other):
return isinstance(other, And) and self.conjuncts == other.conjuncts
def __hash__(self):
return hash(
("and", tuple(hash(conjunct) for conjunct in self.conjuncts))
)
def __repr__(self):
conjunctions = ", ".join(
[str(conjunct) for conjunct in self.conjuncts]
)
return f"And({conjunctions})"
def add(self, conjunct):
Sentence.validate(conjunct)
self.conjuncts.append(conjunct)
def evaluate(self, model):
return all(conjunct.evaluate(model) for conjunct in self.conjuncts)
def formula(self):
if len(self.conjuncts) == 1:
return self.conjuncts[0].formula()
return " ∧ ".join([Sentence.parenthesize(conjunct.formula())
for conjunct in self.conjuncts])
def symbols(self):
return set.union(*[conjunct.symbols() for conjunct in self.conjuncts])
class Or(Sentence):
def __init__(self, *disjuncts):
for disjunct in disjuncts:
Sentence.validate(disjunct)
self.disjuncts = list(disjuncts)
def __eq__(self, other):
return isinstance(other, Or) and self.disjuncts == other.disjuncts
def __hash__(self):
return hash(
("or", tuple(hash(disjunct) for disjunct in self.disjuncts))
)
def __repr__(self):
disjuncts = ", ".join([str(disjunct) for disjunct in self.disjuncts])
return f"Or({disjuncts})"
def evaluate(self, model):
return any(disjunct.evaluate(model) for disjunct in self.disjuncts)
def formula(self):
if len(self.disjuncts) == 1:
return self.disjuncts[0].formula()
return " ∨ ".join([Sentence.parenthesize(disjunct.formula())
for disjunct in self.disjuncts])
def symbols(self):
return set.union(*[disjunct.symbols() for disjunct in self.disjuncts])
class Implication(Sentence):
def __init__(self, antecedent, consequent):
Sentence.validate(antecedent)
Sentence.validate(consequent)
self.antecedent = antecedent
self.consequent = consequent
def __eq__(self, other):
return (isinstance(other, Implication)
and self.antecedent == other.antecedent
and self.consequent == other.consequent)
def __hash__(self):
return hash(("implies", hash(self.antecedent), hash(self.consequent)))
def __repr__(self):
return f"Implication({self.antecedent}, {self.consequent})"
def evaluate(self, model):
return ((not self.antecedent.evaluate(model))
or self.consequent.evaluate(model))
def formula(self):
antecedent = Sentence.parenthesize(self.antecedent.formula())
consequent = Sentence.parenthesize(self.consequent.formula())
return f"{antecedent} => {consequent}"
def symbols(self):
return set.union(self.antecedent.symbols(), self.consequent.symbols())
class Biconditional(Sentence):
def __init__(self, left, right):
Sentence.validate(left)
Sentence.validate(right)
self.left = left
self.right = right
def __eq__(self, other):
return (isinstance(other, Biconditional)
and self.left == other.left
and self.right == other.right)
def __hash__(self):
return hash(("biconditional", hash(self.left), hash(self.right)))
def __repr__(self):
return f"Biconditional({self.left}, {self.right})"
def evaluate(self, model):
return ((self.left.evaluate(model)
and self.right.evaluate(model))
or (not self.left.evaluate(model)
and not self.right.evaluate(model)))
def formula(self):
left = Sentence.parenthesize(str(self.left))
right = Sentence.parenthesize(str(self.right))
return f"{left} <=> {right}"
def symbols(self):
return set.union(self.left.symbols(), self.right.symbols())
def model_check(knowledge, query):
"""Checks if knowledge base entails query."""
def check_all(knowledge, query, symbols, model):
"""Checks if knowledge base entails query, given a particular model."""
# If model has an assignment for each symbol
if not symbols:
# If knowledge base is true in model, then query must also be true
if knowledge.evaluate(model):
return query.evaluate(model)
return True
else:
# Choose one of the remaining unused symbols
remaining = symbols.copy()
p = remaining.pop()
# Create a model where the symbol is true
model_true = model.copy()
model_true[p] = True
# Create a model where the symbol is false
model_false = model.copy()
model_false[p] = False
# Ensure entailment holds in both models
return (check_all(knowledge, query, remaining, model_true) and
check_all(knowledge, query, remaining, model_false))
# Get all symbols in both knowledge and query
symbols = set.union(knowledge.symbols(), query.symbols())
# Check that knowledge entails query
return check_all(knowledge, query, symbols, dict())
我知道代码太多了，但我的疑惑很简单，我测试了基本的知识布尔代数运算，如NOT、AND、OR。问题仅出在 OR 函数上，如果至少有一个为真，则它始终应该 return 为真。但它 return 是假的。
from logic import *
a = Symbol("a")
b = Symbol("b")
# OR
# Error here
orSentence = Or(a, b)
valueOrSentence = model_check(orSentence, a)
print(orSentence.formula() + f" ({valueOrSentence})")
valueOrSentence = model_check(orSentence, Not(a))
print(orSentence.formula() + f" ({valueOrSentence})")
print('---/---/---/')
检查模型时应该return "true"，但不是 returning "false"
我更愿意相信哈佛 logic.py 文件没有错误，我应该怎么做才能解决这个“或”逻辑？
对于 model 的一个特定情况，您的 knowledge 包含但 query 不包含，因此它是 returning False。没毛病。
当 model = {'a': False, 'b': True} 那么 orSentence.evaluate(model) 会 return True 但 a.evaluate(model) 会 return False model_check 作为 False.
如果您使用 andSentence = And(a, b) 然后 运行 model_check(andSentence, a)，它将 return True 因为对于 model 的每个值要么 andSentence（知识）和a（查询）都是True或者都是False.
希望它澄清！
我正在学习哈佛的 Python 人工智能概论课程。我很享受。但是我下载了逻辑文件以使用布尔代数和知识，即简单的操作（或，与，非...）在我表示怀疑之前，我将分享来自哈佛源代码的知识class，我希望没有'关于它的问题：
link 到这个 class:
logic.py
import itertools
class Sentence():
def evaluate(self, model):
"""Evaluates the logical sentence."""
raise Exception("nothing to evaluate")
def formula(self):
"""Returns string formula representing logical sentence."""
return ""
def symbols(self):
"""Returns a set of all symbols in the logical sentence."""
return set()
@classmethod
def validate(cls, sentence):
if not isinstance(sentence, Sentence):
raise TypeError("must be a logical sentence")
@classmethod
def parenthesize(cls, s):
"""Parenthesizes an expression if not already parenthesized."""
def balanced(s):
"""Checks if a string has balanced parentheses."""
count = 0
for c in s:
if c == "(":
count += 1
elif c == ")":
if count <= 0:
return False
count -= 1
return count == 0
if not len(s) or s.isalpha() or (
s[0] == "(" and s[-1] == ")" and balanced(s[1:-1])
):
return s
else:
return f"({s})"
class Symbol(Sentence):
def __init__(self, name):
self.name = name
def __eq__(self, other):
return isinstance(other, Symbol) and self.name == other.name
def __hash__(self):
return hash(("symbol", self.name))
def __repr__(self):
return self.name
def evaluate(self, model):
try:
return bool(model[self.name])
except KeyError:
raise Exception(f"variable {self.name} not in model")
def formula(self):
return self.name
def symbols(self):
return {self.name}
class Not(Sentence):
def __init__(self, operand):
Sentence.validate(operand)
self.operand = operand
def __eq__(self, other):
return isinstance(other, Not) and self.operand == other.operand
def __hash__(self):
return hash(("not", hash(self.operand)))
def __repr__(self):
return f"Not({self.operand})"
def evaluate(self, model):
return not self.operand.evaluate(model)
def formula(self):
return "¬" + Sentence.parenthesize(self.operand.formula())
def symbols(self):
return self.operand.symbols()
class And(Sentence):
def __init__(self, *conjuncts):
for conjunct in conjuncts:
Sentence.validate(conjunct)
self.conjuncts = list(conjuncts)
def __eq__(self, other):
return isinstance(other, And) and self.conjuncts == other.conjuncts
def __hash__(self):
return hash(
("and", tuple(hash(conjunct) for conjunct in self.conjuncts))
)
def __repr__(self):
conjunctions = ", ".join(
[str(conjunct) for conjunct in self.conjuncts]
)
return f"And({conjunctions})"
def add(self, conjunct):
Sentence.validate(conjunct)
self.conjuncts.append(conjunct)
def evaluate(self, model):
return all(conjunct.evaluate(model) for conjunct in self.conjuncts)
def formula(self):
if len(self.conjuncts) == 1:
return self.conjuncts[0].formula()
return " ∧ ".join([Sentence.parenthesize(conjunct.formula())
for conjunct in self.conjuncts])
def symbols(self):
return set.union(*[conjunct.symbols() for conjunct in self.conjuncts])
class Or(Sentence):
def __init__(self, *disjuncts):
for disjunct in disjuncts:
Sentence.validate(disjunct)
self.disjuncts = list(disjuncts)
def __eq__(self, other):
return isinstance(other, Or) and self.disjuncts == other.disjuncts
def __hash__(self):
return hash(
("or", tuple(hash(disjunct) for disjunct in self.disjuncts))
)
def __repr__(self):
disjuncts = ", ".join([str(disjunct) for disjunct in self.disjuncts])
return f"Or({disjuncts})"
def evaluate(self, model):
return any(disjunct.evaluate(model) for disjunct in self.disjuncts)
def formula(self):
if len(self.disjuncts) == 1:
return self.disjuncts[0].formula()
return " ∨ ".join([Sentence.parenthesize(disjunct.formula())
for disjunct in self.disjuncts])
def symbols(self):
return set.union(*[disjunct.symbols() for disjunct in self.disjuncts])
class Implication(Sentence):
def __init__(self, antecedent, consequent):
Sentence.validate(antecedent)
Sentence.validate(consequent)
self.antecedent = antecedent
self.consequent = consequent
def __eq__(self, other):
return (isinstance(other, Implication)
and self.antecedent == other.antecedent
and self.consequent == other.consequent)
def __hash__(self):
return hash(("implies", hash(self.antecedent), hash(self.consequent)))
def __repr__(self):
return f"Implication({self.antecedent}, {self.consequent})"
def evaluate(self, model):
return ((not self.antecedent.evaluate(model))
or self.consequent.evaluate(model))
def formula(self):
antecedent = Sentence.parenthesize(self.antecedent.formula())
consequent = Sentence.parenthesize(self.consequent.formula())
return f"{antecedent} => {consequent}"
def symbols(self):
return set.union(self.antecedent.symbols(), self.consequent.symbols())
class Biconditional(Sentence):
def __init__(self, left, right):
Sentence.validate(left)
Sentence.validate(right)
self.left = left
self.right = right
def __eq__(self, other):
return (isinstance(other, Biconditional)
and self.left == other.left
and self.right == other.right)
def __hash__(self):
return hash(("biconditional", hash(self.left), hash(self.right)))
def __repr__(self):
return f"Biconditional({self.left}, {self.right})"
def evaluate(self, model):
return ((self.left.evaluate(model)
and self.right.evaluate(model))
or (not self.left.evaluate(model)
and not self.right.evaluate(model)))
def formula(self):
left = Sentence.parenthesize(str(self.left))
right = Sentence.parenthesize(str(self.right))
return f"{left} <=> {right}"
def symbols(self):
return set.union(self.left.symbols(), self.right.symbols())
def model_check(knowledge, query):
"""Checks if knowledge base entails query."""
def check_all(knowledge, query, symbols, model):
"""Checks if knowledge base entails query, given a particular model."""
# If model has an assignment for each symbol
if not symbols:
# If knowledge base is true in model, then query must also be true
if knowledge.evaluate(model):
return query.evaluate(model)
return True
else:
# Choose one of the remaining unused symbols
remaining = symbols.copy()
p = remaining.pop()
# Create a model where the symbol is true
model_true = model.copy()
model_true[p] = True
# Create a model where the symbol is false
model_false = model.copy()
model_false[p] = False
# Ensure entailment holds in both models
return (check_all(knowledge, query, remaining, model_true) and
check_all(knowledge, query, remaining, model_false))
# Get all symbols in both knowledge and query
symbols = set.union(knowledge.symbols(), query.symbols())
# Check that knowledge entails query
return check_all(knowledge, query, symbols, dict())
我知道代码太多了，但我的疑惑很简单，我测试了基本的知识布尔代数运算，如NOT、AND、OR。问题仅出在 OR 函数上，如果至少有一个为真，则它始终应该 return 为真。但它 return 是假的。
from logic import *
a = Symbol("a")
b = Symbol("b")
# OR
# Error here
orSentence = Or(a, b)
valueOrSentence = model_check(orSentence, a)
print(orSentence.formula() + f" ({valueOrSentence})")
valueOrSentence = model_check(orSentence, Not(a))
print(orSentence.formula() + f" ({valueOrSentence})")
print('---/---/---/')
检查模型时应该return "true"，但不是 returning "false"
我更愿意相信哈佛 logic.py 文件没有错误，我应该怎么做才能解决这个“或”逻辑？
对于 model 的一个特定情况，您的 knowledge 包含但 query 不包含，因此它是 returning False。没毛病。
当 model = {'a': False, 'b': True} 那么 orSentence.evaluate(model) 会 return True 但 a.evaluate(model) 会 return False model_check 作为 False.
如果您使用 andSentence = And(a, b) 然后 运行 model_check(andSentence, a)，它将 return True 因为对于 model 的每个值要么 andSentence（知识）和a（查询）都是True或者都是False.
希望它澄清！