| 单词 | syntactic consequence |
| 释义 | > as lemmassyntactic consequence syntactic consequence n. Logic the relationship by which, in a particular formal logical system, a sentence can be derived from others by the inference rules of the system, without regard to the truth or interpretation of the sentences; logical consequence conceived syntactically, as in proof theory, rather than semantically, as in model theory; (also) a sentence which is derivable from others by the inference rules of a particular formal logical system; often contrasted with semantic consequence n. at semantic adj. Compounds. ΚΠ 1964 Newman-Studien 6 80 (note) Strictly speaking, we are dealing with syntactic consequence in this example and not with material implication. 1967 G. Kreisel in I. Lakatos Probl. Philos. Math. I. 139 Section 2 deals with the relation between intuitive logical consequence on the one hand and so-called semantic resp. syntactic consequence on the other. 1982 Mind 91 222 A soundness proof for a deductive system L establishes that if B is a syntactic consequence of A according to the axioms and/or rules of L, then B is also a semantic consequence of A in L. 2000 Z. Pawlak et al. in L. Polkowski et al. Rough Set Methods & Applic. xii. 595 With a logic we associate therefore two basic relations: the relation of syntactic consequence denoted ⊢, and the relation of semantic consequence (entailment) denoted ⊨. 2012 D. Papineau Philos. Devices iv. xi. 151 If [in propositional logic] one sentence is a syntactic consequence of some others (that is, it is provable from them), then it must be a semantic consequence too (that is, its truth must be guaranteed by their truth). < as lemmas |
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