Initial commit.

logic.py

@@ -0,0 +1,263 @@
+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())

puzzle.py

@@ -0,0 +1,80 @@
+from logic import *
+
+AKnight = Symbol("A is a Knight")
+AKnave = Symbol("A is a Knave")
+
+BKnight = Symbol("B is a Knight")
+BKnave = Symbol("B is a Knave")
+
+CKnight = Symbol("C is a Knight")
+CKnave = Symbol("C is a Knave")
+
+# Puzzle 0
+# A says "I am both a knight and a knave."
+knowledge0 = And(
+	Or(AKnave, AKnight),
+	And(AKnave, Not(AKnight)),
+	Implication(And(AKnight, AKnave), AKnave) 
+)
+
+# Puzzle 1
+# A says "We are both knaves."
+# B says nothing.
+knowledge1 = And(
+	Or(AKnave, AKnight),
+	Or(BKnave, BKnight),
+	Or(And(AKnave, BKnight), And(AKnave, BKnave)),
+	Implication(And(AKnave, BKnave), And(AKnave, BKnight))
+)
+
+# Puzzle 2
+# A says "We are the same kind."
+# B says "We are of different kinds."
+knowledge2 = And(
+	Or(And(AKnave, BKnave), And(AKnight, BKnight), And(AKnave, BKnight)),
+	Biconditional(AKnave, Not(AKnight)),
+	Biconditional(BKnave, Not(BKnight)),
+	Implication(AKnave, Not(And(AKnave, BKnave))),
+	Implication(BKnight, And(AKnave, BKnight))
+)
+
+# Puzzle 3
+# A says either "I am a knight." or "I am a knave.", but you don't know which.
+# B says "A said 'I am a knave'."
+# B says "C is a knave."
+# C says "A is a knight."
+knowledge3 = And(
+	Or(AKnave, AKnight),
+	Or(BKnave, BKnight),
+	Or(CKnave, CKnight),
+	Biconditional(AKnave, Not(AKnight)),
+	Biconditional(BKnave, Not(BKnight)),
+	Biconditional(CKnave, Not(CKnight)),
+	
+	Implication(AKnave, Not(AKnave)),
+	Implication(BKnight, And(AKnave, CKnave)),
+	Implication(BKnave, And(AKnight, CKnight)),
+	Implication(CKnight, And(AKnight, BKnave))
+)
+
+
+def main():
+	symbols = [AKnight, AKnave, BKnight, BKnave, CKnight, CKnave]
+	puzzles = [
+		("Puzzle 0", knowledge0),
+		("Puzzle 1", knowledge1),
+		("Puzzle 2", knowledge2),
+		("Puzzle 3", knowledge3)
+	]
+	for puzzle, knowledge in puzzles:
+		print(puzzle)
+		if len(knowledge.conjuncts) == 0:
+			print("    Not yet implemented.")
+		else:
+			for symbol in symbols:
+				if model_check(knowledge, symbol):
+					print(f"    {symbol}")
+
+
+if __name__ == "__main__":
+	main()

readme.md

@@ -0,0 +1,3 @@
+Homework that I did for an AI class that Harvard offered. Sadly I 
+never got a chance to finish said class, but I figured these early projects 
+would be worth archiving.