(4) Each argument bears one and only one θ-role, and each θ-role is assigned to one and only one argument. I will refer to (4) as the "θ-criterion". An argument is assigned a θ-role by virtue of the θ-position that it or its trace occupies in LF.
- Chomsky (1993), a pag.36

[…] "θ-criterion": Given the structure "S", there is a set K of chains, K = {Ci}, where Ci = (αi 1,...,αi n), such that: (i) if α is an argument of "S", then there is a Ci ∈K such that α = αij and a θ-role is assigned to Ci by exactly one position "P". (ii) if "P" is a position of "S" marked with the θ-role "R", then there is a Ci ∈K to which "P" assigns "R", and exactly one αij in Ci is an argument. In case (i), α has the θ-role assigned by "P" [...] the θ-criterion requires that arguments be distributed properly in the configurations that are jointly determined by the projection principle and by principles of the categorial component of the base, including those idiosyncratic properties that are stipulated by rule [...] and those determined by general principle. The θ-criterion must be met at LF, and by the projection principle, at D- and S-structure as well. The θ-criterion is satisfied in essentially the same way at S-structure and LF.
- Chomsky (1993), a pag.335