Semigroups in Classical Planning

Classical planning has become a major paradigm in areas of applied computer science,
such as robotics, logistics and manufacturing. Although the class of programs under its scope (classical plans) are strikingly simple, current research still depends on traditional formalisms that are largely disconnected from abstract mathematics. (An exception being recent attempts to subsume planning, combined with computer vision or reasoning, into category theory.)
To this end, we suggest an algebraic appropach to classical planning that: (1) brings this area closer to mathematical practice; and (2) permits an abstract approach to plans that benefits research in the area of classical planning itself.