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In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, [1] or simplification) [2][3][4] is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true. The rule makes it possible to shorten longer proofs ...
Transformation rules. In propositional logic, disjunction elimination[1][2] (sometimes named proof by cases, case analysis, or or elimination) is the valid 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 implies a statement and a statement ...
Rules of inference are syntactical transform rules which one can use to infer a conclusion from a premise to create an argument. A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following ...
In propositional logic, modus ponens (/ ˈmoʊdəsˈpoʊnɛnz /; 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.
Fitch's paradox of knowability is a puzzle of epistemic logic. It provides a challenge to the knowability thesis, which states that every truth is, in principle, knowable. The paradox states that this assumption implies the omniscience principle, which asserts that every truth is known. Essentially, Fitch's paradox asserts that the existence of ...
In propositional logic, tautology is either of two commonly used rules of replacement. [1][2][3] The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs. They are: The principle of idempotency of disjunction: and the principle of idempotency of conjunction: Where " " is a metalogical symbol ...
Venn diagram of. In logic, mathematics and linguistics, and ( ) is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as 1 or or (prefix) or or 2 in which is the most modern and widely used. The and of a set of operands is true if and only if all of its operands ...
Conjunction introduction (often abbreviated simply as conjunction and also called and introduction or adjunction) [1][2][3] is a 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 the proposition is true, and the proposition is true, then the ...