päättelysääntö

Päättelysääntö, known in English as an inference rule, is a logical principle that allows one to derive conclusions from premises. In formal logic systems, such as propositional and first‑order logic, inference rules are the fundamental mechanisms by which proof trees or derivations are constructed. The most common primary rule is modus ponens, which states that from "If P then Q" and P, one may infer Q. Other essential rules include modus tollens, disjunctive syllogism, and hypothetical syllogism, each providing a distinct pattern for valid reasoning.

Inference rules can be categorized into sound and unsound forms. Sound rules preserve truth: if the premises are true, so is the conclusion. Soundness is a key property ensuring that formal proofs correspond to valid reasoning in the intended semantics. In contrast, a rule that is not sound may produce false conclusions from true premises, and as such, it is generally excluded from rigorous deductive systems.

The use of inference rules extends beyond pure logic into computer science, where they underpin automated theorem proving, type checking, and formal verification. In programming language semantics, rules such as evaluation contexts and reduction relations are often treated as inference rules. Consequently, päättelysääntö plays a pivotal role in both theoretical foundations and practical applications of logical reasoning.