“disjunction”的概念、定义、翻译、参考文献-科学参考

disjunction

Mathematics

See exclusive disjunction, inclusive disjunction. The common usage of the term ‘or’ where the compound sentence is true if at least one of the parts is true is inclusive disjunction.

Computer

A logical expression of the form
$a_{1} \lor a_{2} \lor \dots \lor a_{n}$
where ∨ is the OR operation. A particular disjunction of interest is the disjunctive normal form of a Boolean expression involving n variables, x₁, x₂,…, x_n. Each a_i is then of the form
$(y_{1} \land y_{2} \land \dots y_{n})$
where ∧ is the AND operation and each y_i is equal to x_i or the complement of x_i. Reducing expressions to disjunctive normal form provides a ready method of determining the equivalence of two Boolean expressions. See also propositional calculus. Compare conjunction.

Logic

A logical connective representing central features of the natural language ‘or’. Standardly, the formal truth condition for disjunction is:
- • $φ \lor ψ$ is true if and only if either $φ$ is true or $ψ$ is true.
Connectives described as disjunction are sometimes encountered for which the above truth condition does not hold. For example, the relevant logic connective of fusion—in which $φ + ψ$ is treated as an intensional disjunction—requires not that both $φ$ and $ψ$ are true, but that the negation of $φ$ entails the truth of $ψ$ and that the negation of $ψ$ entails the truth of $φ$ .

Philosophy

The statement that at least one of two propositions is true: it thus corresponds to ‘p or q’. Inclusive disjunction allows that both may be true; exclusive disjunction that one but not both is true. In the propositional calculus disjunction is treated as a truth function.

单词	disjunction
释义	disjunction Mathematics See exclusive disjunction, inclusive disjunction. The common usage of the term ‘or’ where the compound sentence is true if at least one of the parts is true is inclusive disjunction. Computer A logical expression of the form $a_{1} \lor a_{2} \lor \dots \lor a_{n}$ where ∨ is the OR operation. A particular disjunction of interest is the disjunctive normal form of a Boolean expression involving n variables, x₁, x₂,…, x_n. Each a_i is then of the form $(y_{1} \land y_{2} \land \dots y_{n})$ where ∧ is the AND operation and each y_i is equal to x_i or the complement of x_i. Reducing expressions to disjunctive normal form provides a ready method of determining the equivalence of two Boolean expressions. See also propositional calculus. Compare conjunction. Logic A logical connective representing central features of the natural language ‘or’. Standardly, the formal truth condition for disjunction is: • $φ \lor ψ$ is true if and only if either $φ$ is true or $ψ$ is true. Connectives described as disjunction are sometimes encountered for which the above truth condition does not hold. For example, the relevant logic connective of fusion—in which $φ + ψ$ is treated as an intensional disjunction—requires not that both $φ$ and $ψ$ are true, but that the negation of $φ$ entails the truth of $ψ$ and that the negation of $ψ$ entails the truth of $φ$ . Philosophy The statement that at least one of two propositions is true: it thus corresponds to ‘p or q’. Inclusive disjunction allows that both may be true; exclusive disjunction that one but not both is true. In the propositional calculus disjunction is treated as a truth function.
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