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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."
14, OR, Logical disjunction; 15, true, Tautology. Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.
A conjunctive grammar is defined by the 4-tuple = (,,,) where V is a finite set; each element v ∈ V {\displaystyle v\in V} is called a nonterminal symbol or a variable . Each variable represents a different type of phrase or clause in the sentence.
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
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 ...
In logic, a clause is a propositional formula formed from a finite collection of literals (atoms or their negations) and logical connectives.A clause is true either whenever at least one of the literals that form it is true (a disjunctive clause, the most common use of the term), or when all of the literals that form it are true (a conjunctive clause, a less common use of the term).
Disjunction in natural languages does not precisely match the interpretation of in classical logic. Notably, classical disjunction is inclusive while natural language disjunction is often understood exclusively, as the following English example typically would be. [1] Mary is eating an apple or a pear.
Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).