What is adequacy in logic?

In logic, adequacy refers to the ability of a set of axioms or rules to derive all necessary theorems within a given system. A logical system is considered adequate if every statement that is true in the intended interpretation can be proven using its axioms and inference rules. This concept is crucial for ensuring that a logical framework is robust enough to capture the intended semantics and reasoning processes. In essence, adequacy ensures that the system is comprehensive and effective for its purpose.