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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.
Modus ponens (also known as "affirming the antecedent" or "the law of detachment") is the primary deductive rule of inference. It applies to arguments that have as first premise a conditional statement ( P → Q {\displaystyle P\rightarrow Q} ) and as second premise the antecedent ( P {\displaystyle P} ) of the conditional statement.
Theorems are those logical formulas where is the conclusion of a valid proof, [4] while the equivalent semantic consequence indicates a tautology.. The tautology rule may be expressed as a sequent:
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
Legal syllogism is a legal concept concerning the law and its application, specifically a form of argument based on deductive reasoning and seeking to establish whether a specified act is lawful. [1] A syllogism is a form of logical reasoning that hinges on a question, a major premise, a minor premise and a conclusion.
Modus ponens is a mixed hypothetical syllogism and is closely related to another valid form of argument, modus tollens. Both have apparently similar but invalid forms: affirming the consequent and denying the antecedent. Constructive dilemma is the disjunctive version of modus ponens. The history of modus ponens goes back to antiquity. [4]
De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.
The name "disjunctive syllogism" derives from its being a syllogism, a three-step argument, and the use of a logical disjunction (any "or" statement.) For example, "P or Q" is a disjunction, where P and Q are called the statement's disjuncts .