Deductive reasoning

Deductive reasoning is inference in which a conclusion follows necessarily from premises when the premises are true and the reasoning is valid.

Logical validity: An argument is logically valid when its conclusion cannot be false if all its premises are true. Validity is the defining link between deductive premises and their guaranteed conclusion.
Premise: A premise is a statement offered as support for a conclusion in an argument. Deductive guarantees are conditional on the truth of the premises.
Inductive reasoning: Inductive reasoning draws generalizations or predictions that premises support without guaranteeing. Unlike deduction, induction can have true premises and a false conclusion.
Mathematical proof: A mathematical proof is a finite or otherwise rigorously specified derivation establishing a mathematical claim from accepted assumptions. Proofs use deductive steps to establish theorems from axioms and prior results.
Soundness: An argument is sound when it is valid and all its premises are true. Soundness adds true premises to the validity required for successful deduction.
Conclusion: A conclusion is the statement an argument aims to establish from its premises. Deduction assesses whether premises necessitate this statement.
Abductive reasoning: Abductive reasoning infers a plausible explanation for observed evidence. Abduction selects explanatory hypotheses rather than conclusions entailed by premises.
Theorem: A theorem is a mathematical proposition established by proof within a theory. A theorem records a conclusion deduced from a theory’s assumptions.
Inference rule: An inference rule is a licensed pattern for deriving conclusions from premises. Rules such as modus ponens make valid deductive steps explicit.
Argument: An argument is a set of statements in which premises are offered to support a conclusion. Deductive reasoning is one way arguments can support their conclusions.

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