# WIKI

## Inference Rules

<https://en.wikipedia.org/wiki/Premise> <https://en.wikipedia.org/wiki/First-order_logic> <https://en.wikipedia.org/wiki/Higher-order_logic> <https://en.wikipedia.org/wiki/Zeroth-order_logic> <https://en.wikipedia.org/wiki/Propositional_calculus> <https://en.wikipedia.org/wiki/Syllogism> <https://en.wikipedia.org/wiki/Law_of_thought>

<https://en.wikipedia.org/wiki/Affirming_a_disjunct> <https://en.wikipedia.org/wiki/Disjunction_elimination> <https://en.wikipedia.org/wiki/Disjunctive_syllogism> <https://en.wikipedia.org/wiki/Hypothetical_syllogism> <https://en.wikipedia.org/wiki/Modus_ponendo_tollens> <https://en.wikipedia.org/wiki/Modus_ponens> <https://en.wikipedia.org/wiki/Reductio_ad_absurdum>

## List of inference rules

Rule of inference <https://en.wikipedia.org/wiki/Rule_of_inference>

[Propositional calculus](https://en.wikipedia.org/wiki/Propositional_calculus) [Predicate logic](https://en.wikipedia.org/wiki/First-order_logic)

### List of inference rules of Propositional logic

Implication [Implication introduction](https://en.wikipedia.org/wiki/Conditional_proof) [elimination (modus ponens)](https://en.wikipedia.org/wiki/Modus_ponens)

Biconditional [Biconditional introduction](https://en.wikipedia.org/wiki/Biconditional_introduction) [elimination](https://en.wikipedia.org/wiki/Biconditional_elimination)

Conjunction [Conjunction introduction](https://en.wikipedia.org/wiki/Conjunction_introduction) [elimination](https://en.wikipedia.org/wiki/Conjunction_elimination)

Disjunction [Disjunction introduction](https://en.wikipedia.org/wiki/Disjunction_introduction) [elimination](https://en.wikipedia.org/wiki/Disjunction_elimination) [Disjunctive](https://en.wikipedia.org/wiki/Disjunctive_syllogism) [hypothetical syllogism](https://en.wikipedia.org/wiki/Hypothetical_syllogism) [Constructive](https://en.wikipedia.org/wiki/Constructive_dilemma) [destructive dilemma](https://en.wikipedia.org/wiki/Destructive_dilemma)

\[Absorption]\(<https://en.wikipedia.org/wiki/Absorption_(logic>)) [modus tollens](https://en.wikipedia.org/wiki/Modus_tollens) [modus ponendo tollens](https://en.wikipedia.org/wiki/Modus_ponendo_tollens)

[Rules of replacement](https://en.wikipedia.org/wiki/Rule_of_replacement) [Associativity](https://en.wikipedia.org/wiki/Associative_property) [Commutativity](https://en.wikipedia.org/wiki/Commutative_property) [Distributivity](https://en.wikipedia.org/wiki/Distributive_property) [Double negation](https://en.wikipedia.org/wiki/Double_negation) [De Morgan's laws](https://en.wikipedia.org/wiki/De_Morgan's_laws) \[Transposition]\(<https://en.wikipedia.org/wiki/Transposition_(logic>)) \[Material implication]\(<https://en.wikipedia.org/wiki/Material_implication_(rule_of_inference>)) \[Exportation]\(<https://en.wikipedia.org/wiki/Exportation_(logic>)) \[Tautology]\(<https://en.wikipedia.org/wiki/Tautology_(rule_of_inference>)) [Negation introduction](https://en.wikipedia.org/wiki/Negation_introduction)

### List of inference rules of Predicate logic

[Universal generalization](https://en.wikipedia.org/wiki/Universal_generalization) [instantiation](https://en.wikipedia.org/wiki/Universal_instantiation) [Existential generalization](https://en.wikipedia.org/wiki/Existential_generalization) [instantiation](https://en.wikipedia.org/wiki/Existential_instantiation)
