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The study defines and analyzes structural resolution in the context of the Modal-Dependence Calculus.

May 6, 2026Open Access

Resolution Properties of the Evaluation Operator

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The study defines and analyzes structural resolution in the context of the Modal-Dependence Calculus.
Defined structural resolution as a system-level property.
Examined the relationship between resolution and the output of the evaluation operator.
Analyzed conditions leading to resolution failure in relation to dependence paths.
Established that resolution occurs if a structure is admissible.
Identified resolution failure as linked to undefined dependence paths.
Found that the failure state remains unchanged when the structure is extended.

Abstract

This paper defines structural resolution as a system-level property in the Modal-Dependence Calculus. Resolution is identified with the output of the evaluation operator, such that a structure is resolved if and only if it is admissible. The analysis establishes that resolution failure occurs whenever a single element lacks a defined dependence path, and that this failure state is invariant under extension of the structure. These results show that resolution is a binary, non-compensatory property determined entirely by element-level definability.

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Austin Jacobs (Mon,) studied this question.

www.synapsesocial.com/papers/69faa30204f884e66b5339d2 — DOI: https://doi.org/10.5281/zenodo.20019240

Resolution Properties of the Evaluation Operator

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