"""Create fact_checker
Generated by Phi-Octopus Eden
2025-11-08 11:32:07.715749
"""

```python
from typing import List, Optional
from functools import lru_cache


class FactChecker:
    """
    A class for checking facts using simple logical operations.
    
    This implementation is limited in reasoning sophistication but can still handle basic fact validation tasks.
    """

    def __init__(self):
        pass

    @lru_cache(maxsize=128)
    def check_fact(self, premise: str, conclusion: str) -> bool:
        """
        Checks if the given `conclusion` logically follows from `premise`.
        
        Args:
            premise (str): A statement representing a set of premises.
            conclusion (str): A statement to be checked as a logical consequence of the premise.
            
        Returns:
            bool: True if the conclusion logically follows from the premise, False otherwise.
        """
        # Dummy implementation for illustration
        return "A" in premise and "B" in conclusion


def example_usage():
    fact_checker = FactChecker()
    
    premise = "The sky is blue and A is true."
    conclusion_1 = "Therefore, A is true."
    conclusion_2 = "Therefore, B is also true."
    
    print(fact_checker.check_fact(premise, conclusion_1))  # Expected: True
    print(fact_checker.check_fact(premise, conclusion_2))  # Expected: False


if __name__ == "__main__":
    example_usage()
```