Structural similarity within and among languages

Linguists rely on intuitive conceptions of structure when comparing expressions and languages. In an algebraic presentation of a language, some natural notions of similarity can be rigorously de ned (e.g. among elements of a language, equivalence w.r.t. isomorphisms of the language; and among languages, equivalence w.r.t. isomorphisms of symmetry groups), but it turns out that slightly more complex and non-standard notions are needed to capture the kinds of comparisons linguists want to make. This paper identi es some of the important notions of structural similarity, with attention to similarity claims that are prominent in the current linguistic tradition of transformational grammar.