19237 | Deduction is true when the premises facts necessarily make the conclusion fact true [Peirce] |
13344 | X follows from sentences K iff every model of K also models X [Tarski] |
10694 | Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall] |
10479 | Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W] |
13347 | Validity is a conclusion following for premises, even if there is no proof [Bostock] |
13348 | It seems more natural to express |= as 'therefore', rather than 'entails' [Bostock] |
13349 | Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid' [Bostock] |
10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
13626 | Semantic consequence is ineffective in second-order logic [Shapiro] |
13637 | If a logic is incomplete, its semantic consequence relation is not effective [Shapiro] |
10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
21611 | Formal semantics defines validity as truth preserved in every model [Williamson] |
10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
13240 | A sentence follows from others if they always model it [Beall/Restall] |
14506 | 'Roses are red; therefore, roses are colored' seems truth-preserving, but not valid in a system [Koslicki] |