Linked from

The 37 pages that link to Rule of inference, each with the reason it gives.

• Mathematical proofRelated: Each proof step must preserve truth under an accepted rule of inference.

• Deductive reasoningRelated: Rules such as modus ponens make valid deductive steps explicit.

• AxiomRelated: Inference rules determine what a theory can prove from its axioms.

• Type theoryRelated: Type theories use inference rules to define valid formation and typing steps.

• Logical consequenceNarrower topic: Inference rules generate syntactic consequence step by step.

• Sequent calculusNarrower topic: Each calculus step applies a rule to derive a new sequent.

• Formal proofRelated: Each proof step is licensed by an inference rule.

• Proof theoryRelated: Inference rules determine which steps count as valid in a formal derivation.

• ConsistencyRelated: A theory’s permitted inference rules help determine what its axioms entail.

• Mathematical logicRelated: Inference rules define the permitted steps in a formal proof.

• Modus ponensNarrower topic: Modus ponens is one member of this broader family of proof rules.

• SoundnessRelated: A system's rules determine whether its proofs preserve truth.

• Formal systemRelated: Inference rules license each step in a formal derivation.

• Proof assistantRelated: The assistant checks that each proof step follows permitted inference rules.

• Formal logicRelated: Inference rules provide the permitted steps in formal derivations.

• Axiomatic methodRelated: Inference rules determine which steps from axioms to theorems count as valid.

• FormalismRelated: It licenses each step in a formal proof independently of interpretation.

• Modus tollensNarrower topic: Modus tollens is one such pattern, distinguished by its conditional and negative premise.

• DerivationRelated: In logical derivations, inference rules justify transitions between statements.

• LogicRelated: Inference rules make valid steps explicit in a formal derivation.

• Conditional proofNarrower topic: Conditional proof is an application of a rule governing valid derivations.

• DemonstrationRelated: Demonstrations proceed by applying rules that preserve necessary consequence.

• Logical formRelated: Rules give formal procedures for deriving conclusions from argument structures.

• Axiom schemaCompared with: An axiom schema supplies starting statements; an inference rule licenses steps from premises.

• Axiomatic systemBroader topic: Inference rules determine which steps count as valid derivations in the system.

• Deductive systemBroader topic: Inference rules are the system's basic steps for extending a derivation.

• Disjunction introductionNarrower topic: Disjunction introduction specifies one permitted step from premise to conclusion.

• Formal scienceBroader topic: Inference rules determine which deductions a formal system permits.

• Automated reasoningBroader topic: Reasoning systems repeatedly apply these rules to obtain new statements.

• Axiom (general principle)Related: Inference rules determine what follows from accepted axioms.

• Biconditional introductionNarrower topic: This rule is a specific instance of an inference rule.

• Conjunction introductionNarrower topic: Conjunction introduction is a particular rule in this broader family.

• Conjunction eliminationNarrower topic: Conjunction elimination is a particular rule governing permissible deductions.

• Constructive dilemmaNarrower topic: Constructive dilemma is one particular schema for deriving a conclusion from premises.

• Axiom (mathematics and logic)Related: Inference rules turn axioms into theorems by specifying valid steps of deduction.

• Concepts & principlesRelated: Such rules specify how principles may be used in valid arguments.

• Monotonicity of entailmentRelated: The rules of a system determine whether adding premises preserves derivability.