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Authors' ORCIDs

Hafiz Burhan Ul Haq: https://orcid.org/0000-0003-3026-3728

Muhammad Nauman Irshad: https://orcid.org/0000-0003-1782-4658

Article Type

Research Article

Abstract

This paper introduces Generative Endurance Logic (GEL), a formal framework for studying objects through the outcomes they can produce. In many cases, an object cannot be judged only by a fixed truth value, score, or utility value. A rule, model, action, or strategy may behave well in one situation but fail when the context changes or when small perturbations occur. GEL addresses this issue by treating each object as a generator of outcomes. Each object a is linked to a generation map Ga:X×Ω→Y, where X is the context space, Ω is the perturbation space, and Y is the outcome space. The value of the object is then derived from the outcomes it generates. The proposed framework defines Endurance value based on four elements: the usefulness of the outcomes generated, their satisfaction of constraints, their Equilibrium under perturbations, and their risk of falling below an acceptable level. These elements are combined into an Endurance function that gives a value in [0,1]. The paper also defines a generative order relation, an Endurance equivalence relation, and a consequence relation based on preserving or improving Endurance. Basic properties such as boundedness, monotonicity, ordering, equivalence, and threshold preservation are proved. The framework provides a simple mathematical basis for reasoning about objects whose value depends not only on what they are, but also on what they are able to generate under changing conditions.

Keywords

Generative endurance logic, Axiomatic logic, Mathematical reasoning, Outcome generation, Endurance functional, Reliability, Equilibrium of perturbations, Collapse risk

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