A (*partial*) *valuation* for a language *S* on a set *T* of *reference points* is a (partial) function *v*: *T* × *S* → {0,1}. A (*partial*) *frame interpretation* for *S* is a couple (*f*, *H*), where *f* is a structure (called *frame*) defined on a set *T* and *H* is a set of (partial) valuations for *S* on *T*. It is *logical* iff (i) if *v* ∈ *H*, *e* is a substitution in *S*, then *v*_{e} ∈ *H*, where *v*_{e}(*t*, *a*) = *v*(*t*, *ea*) and (ii) if *v*,*w* ∈ *H* and *v*(*t*,*p*) = *w*(*t*,*p*) for all*t*and all variables *p*,then *v* = *w*.