Which are needed to compute the logical inference algorithm? A. Logical equivalence B. Validity C. Satisfiability D. All of the mentioned

The correct answer is: All of the mentioned.

Logical equivalence is a relation between two logical expressions that are true under the same conditions. Validity is a property of a logical argument that is

true regardless of the truth values of its premises. Satisfiability is a property of a logical formula that has at least one assignment of truth values to its variables that makes it true.

Logical inference is the process of deriving new conclusions from given premises. In order to compute a logical inference algorithm, we need to be able to determine whether two logical expressions are logically equivalent, whether a logical argument is valid, and whether a logical formula is satisfiable.

Here are some examples of logical equivalence, validity, and satisfiability:

• The logical expressions $p \land q$ and $q \land p$ are logically equivalent.
• The argument “All men are mortal. Socrates is a man. Therefore, Socrates is mortal” is valid.
• The formula $x \lor \neg x$ is satisfiable.

Logical equivalence, validity, and satisfiability are all fundamental concepts in logic. They are used in a variety of applications, including artificial intelligence, computer science, and mathematics.