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In logic and the philosophy of logic, specifically in deductive reasoning, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).
Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.
To include these symbols in the logical formalism, modal logic introduces new rules of inference that govern what role they play in inferences. One rule of inference states that, if something is necessary, then it is also possible. This means that follows from . Another principle states that if a proposition is necessary then its negation is ...
Deductively valid arguments follow a rule of inference. [38] A rule of inference is a scheme of drawing conclusions that depends only on the logical form of the premises and the conclusion but not on their specific content. [39] [40] The most-discussed rule of inference is the modus ponens. It has the following form: p; if p then q; therefore q.
Absorption is a valid argument form and rule of inference of propositional logic. [1] [2] The rule states that if implies , then implies and .The rule makes it possible to introduce conjunctions to proofs.
In propositional logic, modus ponens (/ ˈ m oʊ d ə s ˈ p oʊ n ɛ n z /; MP), also known as modus ponendo ponens (from Latin 'method of putting by placing'), [1] implication elimination, or affirming the antecedent, [2] is a deductive argument form and rule of inference. [3] It can be summarized as "P implies Q. P is true. Therefore, Q must ...
Rule of inference – Systematic logical process capable of deriving a conclusion from hypotheses; List of rules of inference; Theorem – In mathematics, a statement that has been proven; Transduction (machine learning) – Type of statistical inference
In propositional logic, material implication [1] [2] is 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 P implies Q is logically equivalent to not-or and that either form can replace the other in logical proofs.