"""Create logic_validator
Generated by Phi-Octopus Eden
2025-11-08 10:35:23.847778
"""

```python
from typing import List, Callable, Union
from dataclasses import dataclass


@dataclass
class LogicValidator:
    """
    A class to validate logical expressions and check their validity.
    
    Attributes:
        expressions (List[str]): A list of string representations of logic expressions.
        rules (Callable[[str], bool]): A function that evaluates a single logic expression.
    """

    expressions: List[str]
    rules: Callable[[str], bool]

    def __post_init__(self) -> None:
        """
        Post-initialization method to check the validity of each logic expression.
        """
        self.valid_expressions = []
        for expr in self.expressions:
            if self.rules(expr):
                self.valid_expressions.append(expr)
    
    def validate(self) -> List[str]:
        """
        Validate all expressions and return a list of valid ones.

        Returns:
            List[str]: A list of strings representing the valid logic expressions.
        """
        return self.valid_expressions

def is_valid_expression(expression: str) -> bool:
    """
    A function to check if a given logical expression is syntactically correct.
    
    Args:
        expression (str): The string representation of a logic expression.

    Returns:
        bool: True if the expression is valid, False otherwise.
    """
    try:
        # Check if the expression evaluates without error
        eval(expression, {"__builtins__": None}, {})
        return True
    except SyntaxError:
        return False

# Example usage
if __name__ == "__main__":
    expressions = ["(a and b) or not c", "not (x and y)", "(p or q) and r"]
    validator = LogicValidator(expressions, is_valid_expression)
    valid_expressions = validator.validate()
    print("Valid Expressions:", valid_expressions)

```