Transformation rule

Definition

A rule of inference is a way of drawing a conclusion from a set of premises. Also called inference rule and transformation rule, it is a norm of correct inferences that can be used to guide reasoning, justify conclusions, and criticize arguments. As part of deductive logic, rules of inference are argument forms that preserve the truth of the premises, meaning that the conclusion is always true if the premises are true. An inference is deductively valid if it follows a correct rule of inference. Whether this is the case depends only on the form or syntactic structure of the premises and the conclusion, that is, the actual content or concrete meaning of the statements does not affect validity. For instance, modus ponens is a rule of inference that connects two premises of the form "if ${\displaystyle P}$ then ${\displaystyle Q}$" and "${\displaystyle P}$" to the conclusion "${\displaystyle Q}$". The letters ${\displaystyle P}$ and ${\displaystyle Q}$ in this example and in later formulas are so-called metavariables: they stand for any simple or compound proposition. Any argument following modus ponens is valid, independent of the specific meanings of ${\displaystyle P}$ and ${\displaystyle Q}$, such as the argument "If it is day, then it is light. It is day. Therefore, it is light." In addition to 'modus ponens, there are many other rules of inference, such as modus tollens, disjunctive syllogism, and constructive dilemma.