"""Create reasoning_engine
Generated by Phi-Octopus Eden
2025-11-06 06:37:32.153084
"""

```python
from typing import List, Dict

class ReasoningEngine:
    """
    A simple reasoning engine that solves basic constraint satisfaction problems.
    """

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

    def add_constraint(self, variable: str, values: List[int]) -> None:
        """
        Adds a new constraint to the knowledge base.

        :param variable: The name of the variable involved in the constraint.
        :param values: A list of valid values for the variable that satisfy the constraint.
        """
        self.knowledge_base[variable] = values

    def find_solution(self, variables: List[str]) -> Dict[str, int]:
        """
        Attempts to find a solution that satisfies all constraints.

        :param variables: A list of variables to be solved for.
        :return: A dictionary mapping each variable to its value in the solution or an empty dict if no solution exists.
        """
        current_solution = {}
        return self._backtrack(variables, 0, current_solution)

    def _backtrack(self, variables: List[str], index: int, current_solution: Dict[str, int]) -> Dict[str, int]:
        if index == len(variables):
            return current_solution

        variable_to_assign = variables[index]
        for value in self.knowledge_base[variable_to_assign]:
            current_solution[variable_to_assign] = value
            next_state = self._backtrack(variables, index + 1, current_solution)
            if next_state:
                return next_state
        del current_solution[variable_to_assign]

        return {}

# Example usage
if __name__ == "__main__":
    engine = ReasoningEngine()
    engine.add_constraint('x', [1, 2])
    engine.add_constraint('y', [3, 4])
    
    solution = engine.find_solution(['x', 'y'])
    print(f"Solution: {solution}")
```

This code defines a `ReasoningEngine` class that can solve basic constraint satisfaction problems. It includes methods to add constraints and find solutions using a backtracking algorithm. The example usage demonstrates adding simple constraints and finding a solution.