The phrase "conceptual underpinnings" refers to the fundamental ideas or principles that support or form the basis of a concept or theory. Full definition
These explorations also connect artistic processes to the various conceptual underpinnings of each work, including the history of painting and its relationship to the body. (scadmoa.org)
Tworkov, who was born in Biala, Poland, in 1900, was a key member of the first generation of Abstract Expressionists, and in 1949 was a cofounder of the Eighth Street Club, which was one of the central meeting points of the movement, but later in his career he broke from the style, making geometric abstraction with conceptual underpinnings that still sometimes included loose brushstrokes. (jacktworkov.com)