What method involves solving problems using established rules and logic?

Symbolic reasoning is a method that specifically involves applying established rules and logic to solve problems. It focuses on the manipulation of symbols and the relationships between them to derive conclusions, making it particularly useful in fields like mathematics, computer science, and artificial intelligence. By establishing clear rules and definitions, symbolic reasoning allows for systematic problem-solving and the formulation of logical arguments.

In contrast, inference refers to the process of drawing logical conclusions from premises known or assumed to be true. While it does involve some degree of logic, it doesn't solely rely on a set of established rules in the way that symbolic reasoning does. Ethical AI pertains to the development and deployment of artificial intelligence systems in a manner that aligns with ethical guidelines, ensuring fairness, transparency, and accountability. Algorithmic bias addresses the biases that may occur in algorithms, impacting the outputs of AI systems, rather than serving as a structured problem-solving approach. Thus, the aspect of utilizing established rules and logic distinctly aligns with symbolic reasoning.