Search results
Results from the WOW.Com Content Network
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 list, as many of the rules are redundant, and can be proven with the other 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.
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. The rule makes it possible to eliminate a disjunction from a logical proof. It is the rule that
In decision theory, a decision rule is a function which maps an observation to an appropriate action. Decision rules play an important role in the theory of statistics and economics , and are closely related to the concept of a strategy in game theory .
where is a metalogical symbol meaning that is a syntactic consequence of , in the one case, in the other, in some logical system; or as a rule of inference : P ∨ P ∴ P {\displaystyle {\frac {P\lor P}{\therefore P}}}
'He's gotta grow up, man," Tomlin said. "It's an emotional game, man. These divisional games are big. He's got a target on his back because he's George.
Chrysippus seems to have been responsible for introducing the three main types of connectives: the conditional (if), conjunctive (and), and disjunctive (or). [26] A typical conditional takes the form of "if p then q"; [27] whereas a conjunction takes the form of "both p and q"; [27] and a disjunction takes the form of "either p or q". [28]