What is a methodical and logical procedure for solving problems known as?

An algorithm is recognized as a methodical and logical procedure for solving problems because it involves a step-by-step approach that guarantees a solution if followed correctly. Algorithms are often used in mathematics and computer programming, where precise sequences of operations are outlined to arrive at a correct outcome. This systematic nature ensures that different aspects of a problem are carefully considered and evaluated in order to arrive at a definitive answer.

In contrast, heuristics are mental shortcuts that simplify decision-making but do not guarantee a correct solution. Intuition relies on gut feelings or instincts without a structured process, while trial and error involves attempting various solutions until the correct one is found but lacks the systematic approach inherent to algorithms. Thus, the distinction lies in the structured, guaranteed nature of algorithms as opposed to the more flexible and uncertain approaches of the other options.