In formal logic and related fields, a system (such as a set of rules for proof) is considered sound if it cannot prove anything false, and complete if it can prove everything that is true.
- Definition: A proof system is sound if any formula that can be derived (proven) within the system is logically valid (true under all interpretations).
- Guarantee: It ensures that all conclusions reached through the system's rules are correct. You can trust any statement that the system proves.
- Informal: "You can't prove anything that's wrong".
- Example: An argument like "All elephants are pink. Nelly is an elephant. Therefore, Nelly is pink" is valid in its form, but it is not sound because its first premise is false. A sound argument must have both a valid structure and true premises.