Rules of inference are ways of deriving conclusions from premises. They are integral parts of formal logic, serving as norms of the logical structure...

This is a list of rules of inference, logical laws that relate to mathematical formulae. Rules of inference are syntactical transform rules which one can...

BCE). Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic...

structure of the premises and the conclusion follows a pattern called a rule of inference. For example, modus ponens is a rule of inference according...

Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that...

In the field of artificial intelligence, an inference engine is a software component of an intelligent system that applies logical rules to the knowledge...

rule of inference is admissible in a formal system if the set of theorems of the system does not change when that rule is added to the existing rules...

{X} \,Q(x))} A rule of inference is a rule justifying a logical step from hypothesis to conclusion. There are several rules of inference which utilize...

a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that...

elimination, or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "P implies Q. P is true. Therefore, Q must...

valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a logical proof. It is the inference that if...

true, the conclusion could not be false. Valid arguments follow a rule of inference, such as modus ponens or modus tollens. Deductive reasoning plays...

common rule of inference is the rule of substitution. If t is a term and φ is a formula possibly containing the variable x, then φ[t/x] is the result of replacing...

but are of interest for other logics as well. It is defined as a deductive system that generates theorems from axioms and inference rules, especially...

\\\end{aligned}}} A rule of inference is a rule justifying a logical step from hypothesis to conclusion. There are several rules of inference which utilize...

consequence of P ∨ P {\displaystyle P\lor P} , in the one case, P ∧ P {\displaystyle P\land P} in the other, in some logical system; or as a rule of inference: P...

formal proof systems the same conveniency is provided by an explicit inference rule; for example natural deduction calls it implication introduction. In...

mathematical logic, the cut rule is an inference rule of sequent calculus. It is a generalisation of the classical modus ponens inference rule. Its meaning is that...

argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof. It is the inference that if a statement...

Propositional formula Rule of inference Sentence (mathematical logic) Sequent Statement (logic) Subalternation Tautology Theorem Rule of inference (list) Biconditional...

the rule of inference. It differs from a natural language argument in that it is rigorous, unambiguous and mechanically verifiable. If the set of assumptions...

logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive...

Constructive dilemma is a valid rule of inference of propositional logic. It is the inference that, if P implies Q and R implies S and either P or R is...

needed] is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. It...

called or introduction) is a rule of inference of propositional logic and almost every other deduction system. The rule makes it possible to introduce...

or simplification) is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true...

with definitory rules, i.e. with the question of which rules of inference determine whether an argument is valid or not. A separate topic of inquiry concerns...

either axioms, rules of inference, or both as transformation rules for logical expressions in the system. Whereas a rule of inference is always applied...

natural deduction setting is to take as primitive rules of inference negation introduction (from a derivation of P {\displaystyle P} to both Q {\displaystyle...

abduction, abductive inference, or retroduction) is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations...