According to semantic algebra [Wang. 2013] and cognitive linguistics [Wang & Berwick, 2012], any sentence expressed in a natural language is either:

- A semantic equivalence (to-be |=): S |= O

or

- A behavioral denotation (to-do |>): S |> P(O)

where P is a behavioral process, S subject, O object, and P(O) denotes a behavior P applied on O.

Any complex sentences can be treated as a composition of the “to-be” and “to-do” semantics in cognitive linguistics.