“subformula”的概念、定义、翻译、参考文献-科学参考

subformula

Logic

For a formula $φ$ in a recursively constructed language $ℒ$ , any formula $ψ \in ℒ$ an instance of which is employed in the inductive definition of $φ$ , including $φ$ itself. For example, in a language with a binary connective $\land$ , one may have a clause:
- • if $φ$ and $ψ$ are formulae, then $φ \land ψ$ is a formula.
In this case, not only are $φ$ and $ψ$ subformulae of $φ \land ψ$ , but the subformulae of $φ$ and $ψ$ themselves, appearing in the recursive construction of $φ \land ψ$ , are subformulae of $φ \land ψ$ .

单词	subformula
释义	subformula Logic For a formula $φ$ in a recursively constructed language $ℒ$ , any formula $ψ \in ℒ$ an instance of which is employed in the inductive definition of $φ$ , including $φ$ itself. For example, in a language with a binary connective $\land$ , one may have a clause: • if $φ$ and $ψ$ are formulae, then $φ \land ψ$ is a formula. In this case, not only are $φ$ and $ψ$ subformulae of $φ \land ψ$ , but the subformulae of $φ$ and $ψ$ themselves, appearing in the recursive construction of $φ \land ψ$ , are subformulae of $φ \land ψ$ .
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