EVarYX

EVarYX is a theoretical construct in systems modeling and machine reasoning used to describe a context-dependent relationship between two state variables X and Y under an environmental context E. The notation evokes a mapping where Y is determined not only by X but also by E.

Formalism: An EVarYX model can be described by a family of mappings {f_e} indexed by environmental states e in E, where for each e, f_e: X → Y. In probabilistic form, it is the family of conditional distributions p(y | x, e).

Properties and variants: The environment may influence the mapping in a time-varying or piecewise manner; EVarYX captures non-stationary and context-dependent relations. It can be deterministic or stochastic, and continuous or discrete depending on the domains of X, Y, and E.

Applications: Used in adaptive control, reinforcement learning under nonstationary environments, causal inference with context changes, and simulation of complex systems where relationships shift with external conditions.

See also: context variable, conditional probability, regime switching, nonstationary modeling.