"""Create reasoning_engine
Generated by Phi-Octopus Eden
2025-11-05 20:26:32.148149
"""

```python
from typing import List, Dict


class ReasoningEngine:
    """
    A simple reasoning engine to solve problems based on provided rules.
    
    This engine can process a set of rules and use them to infer conclusions from given facts.
    """

    def __init__(self):
        self.rules = {}

    def add_rule(self, rule: str, premise: List[str], conclusion: str) -> None:
        """
        Add a rule to the reasoning engine.

        :param rule: The name of the rule
        :param premise: A list of premises that must be true for the rule to apply
        :param conclusion: The conclusion derived from applying the rule
        """
        if rule not in self.rules:
            self.rules[rule] = {'premises': [], 'conclusions': []}
        self.rules[rule]['premises'].append(premise)
        self.rules[rule]['conclusions'].append(conclusion)

    def apply_rules(self, premises: List[str]) -> Dict[str, str]:
        """
        Apply rules to the given set of premises and return conclusions.

        :param premises: A list of known facts or premises
        :return: A dictionary with applied rule names as keys and derived conclusions as values.
        """
        conclusions = {}
        for rule_name, rule_info in self.rules.items():
            matching_rules = [rule for rule in rule_info['premises'] if set(rule).issubset(set(premises))]
            if matching_rules:
                conclusions[rule_name] = rule_info['conclusions'][rule_info['premises'].index(matching_rules[0])]
        return conclusions

# Example usage
reasoner = ReasoningEngine()
reasoner.add_rule("Rule1", ["P"], "Q")
reasoner.add_rule("Rule2", ["Q"], "R")

print(reasoner.apply_rules(["P"]))  # Should print {'Q': 'R'}
```