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Disjunction introduction or addition (also called or introduction) [1] [2] [3] is a rule of inference of propositional logic and almost every other deduction system. The rule makes it possible to introduce disjunctions to logical proofs. It is the inference that if P is true, then P or Q must be true. An example in English: Socrates is a man.
Implication introduction / elimination (modus ponens) Biconditional introduction / elimination; Conjunction introduction / elimination; Disjunction introduction / elimination; Disjunctive / hypothetical syllogism; Constructive / destructive dilemma; Absorption / modus tollens / modus ponendo tollens; Negation introduction; Rules of replacement
In linguistics, a disjunct is a type of adverbial adjunct that expresses information that is not considered essential to the sentence it appears in, but which is considered to be the speaker's or writer's attitude towards, or descriptive statement of, the propositional content of the sentence, "expressing, for example, the speaker's degree of truthfulness or his manner of speaking."
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
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.
Because the logical or means a disjunction formula is true when either one or both of its parts are true, it is referred to as an inclusive disjunction. This is in contrast with an exclusive disjunction, which is true when one or the other of the arguments are true, but not both (referred to as exclusive or, or XOR).
Venn diagram for "A or B", with inclusive or (OR) Venn diagram for "A or B", with exclusive or (XOR). The fallacy lies in concluding that one disjunct must be false because the other disjunct is true; in fact they may both be true because "or" is defined inclusively rather than exclusively.
Conversely, a disjunction of literals with at most one negated literal is called a dual-Horn clause. A Horn clause with exactly one positive literal is a definite clause or a strict Horn clause ; [ 2 ] a definite clause with no negative literals is a unit clause , [ 3 ] and a unit clause without variables is a fact ; [ 4 ] A Horn clause without ...
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