Rule of inference

A rule of inference specifies how one or more premises can validly yield a conclusion. It preserves validity when applied to true premises within a formal system.

Premise: A proposition assumed or asserted as support for a conclusion in an argument. Inference rules take premises as their inputs.
Modus ponens: An inference rule that derives Q from P and P → Q. It is the standard example of a rule applied to two premises.
Fallacy: A pattern of reasoning that fails to provide the support its conclusion claims. An invalid inference pattern is not a sound rule for deriving conclusions.
Derivation: A finite sequence of formulas in which each line follows from axioms or earlier lines by specified rules. A derivation is built by applying inference rules step by step.
Conclusion: A proposition derived from premises or asserted as the endpoint of an argument. An inference rule specifies which conclusion follows from its premises.
Modus tollens: An inference rule that derives ¬P from P → Q and ¬Q. It shows how a rule can derive a negative conclusion from a conditional and its denied consequent.
Axiom: A formula accepted as a starting point in a formal system without derivation. Unlike an inference rule, an axiom contributes a starting formula rather than a transition.
Soundness: The property that every statement derivable in a formal system is semantically valid. Soundness ensures the system's inference rules do not derive invalid conclusions.
Logical consequence: A relation in which a conclusion must be true whenever its premises are true under a given interpretation. Inference rules are formal ways to derive consequences.
Universal instantiation: An inference rule that derives an instance of a universal statement for a particular object. It licenses replacing a universally quantified variable with a specific term.

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