syntactic consequence造句

Syntactic consequence does not depend on any interpretation of the formal system.
The theorem is a syntactic consequence of all the well formed formulae that in the proof precede it.
The theorem is a syntactic consequence of all the well-formed formulas preceding it in the proof.
In other settings, such as linear logic, the syntactic consequence ( provability ) relation may be used to define the theorems of a system.
where \ vdash is a metalogical symbol meaning that P \ leftrightarrow Q is a syntactic consequence when P \ to Q and Q \ to P are both in a proof;
It's difficult to find syntactic consequence in a sentence. 用syntactic consequence造句挺难的

where \ vdash is a metalogical symbol meaning that Q is a syntactic consequence of P \ to Q, and R \ to Q and P \ or R in some logical system;
where \ vdash is a metalogical symbol meaning that ( \ neg Q \ to \ neg P ) is a syntactic consequence of ( P \ to Q ) in some logical system;
The logically valid formulas of a system are sometimes called the "'theorems "'of the system, especially in the context of first-order logic where G鰀el's completeness theorem establishes the equivalence of semantic and syntactic consequence.
A formula A is a "'syntactic consequence "'within some formal system \ mathcal { FS } of a set of formulas if there is a derivation in formal system \ mathcal { FS } of A from the set .
A formula A is a "'syntactic consequence "'within some formal system \ mathcal { FS } of a set \ Gamma of formulas if there is a formal proof in \ mathcal { FS } of A from the set \ Gamma.
Two formal systems \ mathcal { FS } and \ mathcal { FS'} may have all the same theorems and yet differ in some significant proof-theoretic way ( a formula A may be a syntactic consequence of a formula B in one but not another for instance ).