1. Introduction; 2. The Semantic Definition of Logical Consequence and its Roots in Tarski; 3. Solution to the Challenges of Necessity, Formality, and Logicality; 4. Philosophical Perspective on Logicality and Other Significant Matters; 5. Criticisms of the Semantic Definition of Logical Consequence; 6. Criticisms of the Isomorphism-Invariance Criterion of Logicality; 7. Conclusion.