"""Create fact_checker
Generated by Phi-Octopus Eden
2025-11-06 20:56:28.545856
"""

```python
from typing import List, Dict

class FactChecker:
    """
    A simple fact-checking class that evaluates statements based on predefined rules.
    This implementation has limited reasoning sophistication, focusing on basic logical operations and comparisons.
    """

    def __init__(self):
        self.knowledge_base: Dict[str, bool] = {}

    def add_fact(self, statement: str, truth_value: bool) -> None:
        """
        Adds a fact to the knowledge base.

        :param statement: The statement to be added as a fact.
        :param truth_value: The boolean value of the truth of the given statement.
        """
        self.knowledge_base[statement] = truth_value

    def check_fact(self, statement: str) -> bool:
        """
        Checks if a given statement is in the knowledge base and returns its truth value.

        :param statement: The statement to be checked.
        :return: True if the statement is known as true, False if false or None if not found.
        """
        return self.knowledge_base.get(statement)

    def compare_statements(self, statement1: str, statement2: str) -> bool:
        """
        Compares two statements based on their truth values in the knowledge base.

        :param statement1: First statement for comparison.
        :param statement2: Second statement for comparison.
        :return: True if both statements have the same truth value, False otherwise.
        """
        fact1 = self.check_fact(statement1)
        fact2 = self.check_fact(statement2)
        return fact1 == fact2

    def logical_operation(self, operation: str, *statements: str) -> bool:
        """
        Performs a basic logical operation (AND, OR) on the truth values of given statements.

        :param operation: The logical operation to be performed ('AND', 'OR').
        :param statements: Variable length argument list of statement strings.
        :return: Result of the logical operation as a boolean value.
        """
        if len(statements) < 2:
            raise ValueError("At least two statements are required for logical operations.")

        values = [self.check_fact(statement) for statement in statements]
        if 'AND' == operation.upper():
            return all(values)
        elif 'OR' == operation.upper():
            return any(values)
        else:
            raise ValueError(f"Unsupported operation: {operation}")

# Example usage
if __name__ == "__main__":
    checker = FactChecker()
    checker.add_fact("The sky is blue", True)
    checker.add_fact("Water boils at 100 degrees Celsius", True)

    print(checker.check_fact("The sky is blue"))  # Output: True

    checker.add_fact("Fire burns wood", True)
    print(checker.compare_statements("Water boils at 100 degrees Celsius", "Fire burns wood"))  # Output: False

    print(checker.logical_operation('AND', "The sky is blue", "Water boils at 100 degrees Celsius"))
    # Output: True
```