What question did this study set out to answer?

The research aims to extend the admissibility conditions of the Modal–Dependence Calculus (MDC) concerning structural transformations.

May 5, 2026Open Access

Grounded Persistence and the Conditions of Admissibility under Transformation

Key Points

The research aims to extend the admissibility conditions of the Modal–Dependence Calculus (MDC) concerning structural transformations.
Examined the admissibility condition of transformations within the Modal–Dependence Calculus framework.
Defined admissibility based on the satisfiability of the relation τ(x′) = 1 for resulting elements.
Investigated finite sequences of transformations and their conditions for admissibility.
Admissibility is preserved under transformations only when the definability condition τ(x_i) = 1 is fulfilled at each transformation step.
Transformations yielding τ(x′) = 0 are deemed non-admissible within the calculus framework.

Abstract

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 (xᵢ) = 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.

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