Grounded Persistence and the Conditions of Admissibility under Transformation

This paper extends the admissibility condition of the Modal–Dependence Calculus (MDC) to the domain of structural transformation. A transformation v: x → x′ is admissible if and only if the resultant element satisfies τ(x′) = 1, corresponding to the definability of the dependence relation D*(x′, c). Finite sequences of transformations are admissible if and only if the condition τ(x_i) = 1 holds for all resultant elements. Admissibility is therefore preserved under transformation only when definability is maintained at each step. Any transformation resulting in τ(x′) = 0 yields a non-admissible outcome within the calculus.