Algebra for trees

This chapter presents several algebraic approaches to tree languages. The idea is to design a notion for trees that resembles semigroups or monoids for words. The focus is on the connection between the structure of an algebra recognizing a tree language, and the kind of logic needed to define the tree language. Four algebraic approaches are described in this chapter: trees as terms of universal algebra, preclones, forest algebra, and seminearrings. Each approach is illustrated with an application to logic on trees.