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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. The rule makes it possible to eliminate a disjunction from a logical proof. It is the rule that
Disjunctive syllogism (sometimes abbreviated DS) has one of the same characteristics as modus tollens in that it contains a premise, then in a second premise it denies a statement, leading to the conclusion. In Disjunctive Syllogism, the first premise establishes two options.
Disjunctive / hypothetical syllogism; ... Rules of inference are syntactical transform rules which one can use to infer a conclusion from a premise to create an ...
In the 19th century, modifications to syllogism were incorporated to deal with disjunctive ("A or B") and conditional ("if A then B") statements. Immanuel Kant famously claimed, in Logic (1800), that logic was the one completed science, and that Aristotelian logic more or less included everything about logic that there was to know.
Constructive dilemma [1] [2] [3] 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 true, then either Q or S has to be true.
Disjunctive / hypothetical syllogism; ... The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs. They are:
Disjunctive / hypothetical syllogism; ... inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax
Pages in category "Rules of inference" ... Disjunctive syllogism; Distributive property; Double negation; E. Existential generalization; Existential instantiation;