### Single Idea 10893

#### [catalogued under 5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=]

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.

Gist of Idea

Γ |= φ for sentences if φ is true when all of Γ is true

Source

José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4)

Book Reference

Zalabardo,José L.: 'Introduction to the Theory of Logic' [Westview 2000], p.51

A Reaction

The definition is similar for predicate logic.