AbstractThis paper introduces the novel concepts of semi 2-metric space and interval- valued semi 2-metric space. We establish the fundamental properties of these structures and examine their relationships with existing metric space generalizations. Additionally, it proposes the concept of cubic semi 2-metric spaces by integrating the principles of cubic sets with semi 2-metric spaces. Furthermore, the paper examines the structure of general- ized quasi-pseudometric spaces on L-M -semigroup and investigates the characteristics of the quasi-pseudometric space associated with L-M -semigroup.