Rule of inference facts for kids

A rule of inference is a special kind of rule used in logic. Think of it like a recipe or a guide that helps you figure out new true statements from ones you already know are true. It takes some starting statements, called premises, looks at how they are put together (their syntax), and then gives you a new statement, called a conclusion.

For example, a famous rule of inference is called modus ponens. This rule takes two premises:

• One premise is like saying, "If something is true, then something else must also be true." (For example, "If it rains, then the ground gets wet.")
• The other premise says that the first part of that statement is true. (For example, "It rains.")

If you have these two premises, modus ponens lets you conclude that the second part of the first statement is also true. (So, "The ground gets wet.") This rule works because if the starting statements are true, the conclusion will always be true too.

Rules of inference are very important because they help us make sure our arguments and conclusions are sound and logical. They are like the building blocks for creating strong, truthful arguments.

How Rules of Inference Work

Rules of inference are mostly about the structure of statements, not just what they mean. They look at the pattern of words and symbols. Even though they focus on structure, most rules of inference are designed to preserve truth. This means if your starting premises are true, the conclusion you get by using a valid rule will also be true.

Imagine you have a set of puzzle pieces (your premises). A rule of inference tells you how to connect those pieces to form a new, complete picture (your conclusion). It's a step-by-step way to move from known facts to new discoveries, all while staying logical.

Common Rules in Logic

There are many different rules of inference, especially in different types of logic.

Rules in Propositional Logic

Propositional logic deals with simple statements that can be either true or false. Some popular rules of inference in this area include:

• Modus ponens: As we saw, if "If P then Q" is true, and "P" is true, then "Q" must be true.
• Modus tollens: This rule is a bit like modus ponens but in reverse. If "If P then Q" is true, and "Q" is false, then "P" must also be false. (For example, "If it rains, the ground gets wet." The ground is NOT wet. So, it did NOT rain.)
• Contraposition: This rule says that "If P then Q" is logically the same as "If not Q then not P." It helps you rephrase statements while keeping their meaning.

Rules in Predicate Logic

First-order predicate logic is a more advanced type of logic that deals with things like "all" or "some." It uses rules of inference to handle these ideas, called logical quantifiers. These rules help us make logical jumps when talking about groups of things, not just simple statements.

Images for kids

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  A friendly robot thinking logically.

See also

• In Spanish: Regla de inferencia para niños