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A mixed hypothetical syllogism has two premises: one conditional statement and one statement that either affirms or denies the antecedent or consequent of that conditional statement. For example, If P, then Q. P. ∴ Q. In this example, the first premise is a conditional statement in which "P" is the antecedent and "Q" is the consequent.
The form of a modus tollens argument is a mixed hypothetical syllogism, with two premises and a conclusion: If P, then Q. Not Q. Therefore, not P. The first premise is a conditional ("if-then") claim, such as P implies Q. The second premise is an assertion that Q, the consequent of the conditional claim, is not the
Much like modus ponens and modus tollens, hypothetical syllogism (sometimes abbreviated as HS) contains two premises and a conclusion. It is, however, slightly more complicated than the first two. In short, it states that if one thing happens, another will as well.
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.
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.
Disjunctive / hypothetical syllogism; Constructive / destructive dilemma; ... where is a metalogical symbol meaning that is a syntactic ...
Disjunctive syllogism is closely related and similar to hypothetical syllogism, which is another rule of inference involving a syllogism. It is also related to the law of noncontradiction , one of the three traditional laws of thought .
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.