Persistence Logic

This paper introduces Persistence Logic, a minimal forcing calculus for determining when comparisons can remain coherent under composed admissible variation. Rather than postulating structure in advance, the framework derives which structural elements are unavoidable once incoherent recomposition is excluded. From the requirements of discernibility, admissible variation, and persistence, it shows that accumulated loss, path dependence, transport, and obstruction are forced bookkeeping structures rather than optional modeling choices.

The framework is intentionally non-constructive and boundary-forming. It establishes necessity and exclusion relations without fixing realizations or providing algorithms. A central result is that the general problem of deciding coherence for comparison under composed variation is undecidable, arising intrinsically from the expressive combination of composition, admissible identification, and finite closure. As a result, some comparison tasks cannot be uniformly adjudicated within the calculus.

Persistence Logic therefore functions as a foundational tool for classifying admissible comparison structures and identifying principled limits of formal comparison, with explicit constructions and restricted, decidable regimes developed in companion papers.