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2 ideas
10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
Full Idea: A propositional logic sentence is a 'logical consequence' of a set of sentences (written Γ |= φ) if for every admissible truth-assignment all the sentences in the set Γ are true, then φ is true. | |
From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
A reaction: The definition is similar for predicate logic. |
10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
Full Idea: A formula is the 'logical consequence' of a set of formulas (Γ |= φ) if for every structure in the language and every variable interpretation of the structure, if all the formulas within the set are true and the formula itself is true. | |
From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |