What Is a Rule of Inference?

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  • Written By: H. Bliss
  • Edited By: W. Everett
  • Last Modified Date: 22 January 2019
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In logic and philosophy, the rules of inference refer to a series of rules used to define the parameters for truth in the context of a given situation. They are commonly used in many fields logic and mathematics, and define logical forms or argument forms. Each rule of inference is essentially a different formula for determining the truth of an argument in the given context. A rule of inference can also be called an inference rule.

Rules of inference occur in a great many fields of thought, including logic and mathematics fields like symbolic logic, classical logic and calculus. They are usually guidelines for processing information in that field. For most people, the most well-known set of rules of inference come from propositional logic.

These rules are used within a method of evaluation called natural deduction. Nine basic rules guide proofing of statements under natural deduction. These rules of inference are often expressed using symbols and variables representing the stated conditions. The first few rules of the group are the most widely used. Modus ponens is an if-then argument that states that since the existence of one thing, known as thing O, means that another thing, known as thing A, also exists, the existence of the original thing means that the latter thing logically exists.


The second rule of inference is Modus tollens, also known as denying the consequent. The conjunction introduction is an inference that states that if R is true and I is also true, then R and A are true. The simplification inference is essentially the opposite; it states that if A and R are true, then A is true and R is true. Other rules of inference in logic include the disjunction introduction and elimination, and disjunctive and hypothetical syllogism, as well as biconditional introduction and elimination, and the constructive and destructive dilemma.

When evaluating an argument using a rule of inference, the person evaluating the argument operates on the principle the argued premises are true. The rule of inference is one method of many used in processing the information in a series of statements to figure out whether the information can possibly be true. Learning this method of proofing an argument is helpful on tests that focus on proofing arguments, like the tests needed to enter many advanced degree programs, especially law schools. An alternate method for evaluating the validity of arguments is the truth table.


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