Sorting is still one of the most important problems in Computer Science. Work in transformational programming and automatic program synthesis provided the insight that led to Merritt’s inverted taxonomy of sorting algorithms, a high-level, top-down, conceptually simple and symmetric categorization of sorting algorithms. More recent work in logic-based program synthesis by Lau has produced a logical taxonomy of sorting algorithms. This provides a logical basis for the inverted taxonomy and expands it into a logical inverted taxonomy to include distributive sorting algorithms which can be derived along with comparison-based algorithms. The inclusion of distributive algorithms into a unified conceptual framework is new and significant for a comprehensive perspective on sorting algorithms. In this paper, we describe both the inverted and the logical taxonomies and show how the latter strengthens the latter and expands it into a logical inverted taxonomy of sorting algorithms, a highlevel, top-down, symmetrical paradigm for all sorting algorithms.