Theory¶

The ORE framework treats vulnerability and resilience as distinct but mutually constitutive analytical spaces.

The two frameworks below are provisional organizing structures. They identify two dimensions that recur in resilience analysis:

Operational direction: preserving continuity or producing improvement.
Analytical focus: the current system state or the model, perspective, or operator structure through which future operational possibilities are evaluated.

Resilience framework¶

ORE organizes four resilience capabilities in a (2 times 2) structure:

	System state	Operator model / perspective
Continuity	Robustness Maintaining acceptable operation in the present state under disturbance.	Extensibility Expanding the operational boundary or available capacity across conditions beyond the current state.
Improvement	Rebound Improving performance in the current or recovered state after disruption.	Adaptability Changing the operator model, decision structure, or feasible possibilities to improve future performance.

System state

Operator model / perspective

Continuity

Robustness

Maintaining acceptable operation in the present state under disturbance.

Extensibility

Expanding the operational boundary or available capacity across conditions beyond the current state.

Improvement

Rebound

Improving performance in the current or recovered state after disruption.

Adaptability

Changing the operator model, decision structure, or feasible possibilities to improve future performance.

The terms robustness, rebound, graceful extensibility, and sustained adaptability are in dialogue with Woods’s four concepts for resilience [Woo15, Woo18]. In ORE, the (2 times 2) formulation is a developing formal interpretation of these distinctions, rather than a claim that it reproduces Woods’s terminology or theory exactly.

Vulnerability framework¶

ORE also develops a corresponding (2 times 2) framework for vulnerability. This structure is under active development and will be revised as the formal definition of vulnerability space is completed.

	System state	Operator model / perspective
Exposure or constraint	State vulnerability Vulnerability arising from the system’s present condition, performance, or proximity to an operational boundary.	Model vulnerability Vulnerability arising from the limits, omissions, or assumptions in the model, interpretation, or operator structure.
Consequence or change	Transition vulnerability Vulnerability arising from adverse state transitions or loss of acceptable performance.	Decision vulnerability Vulnerability arising when the available decision model cannot represent, select, or sustain an adequate response.

System state

Operator model / perspective

Exposure or constraint

State vulnerability

Vulnerability arising from the system’s present condition, performance, or proximity to an operational boundary.

Model vulnerability

Vulnerability arising from the limits, omissions, or assumptions in the model, interpretation, or operator structure.

Consequence or change

Transition vulnerability

Vulnerability arising from adverse state transitions or loss of acceptable performance.

Decision vulnerability

Vulnerability arising when the available decision model cannot represent, select, or sustain an adequate response.

Status of the formalism¶

The framework is under active development. Current work concerns formal definitions of vulnerability and resilience spaces; the relationship among states, performance values, feasibility, and decisions; and the role of interpretation and perspective in identifying operational boundaries.

The public descriptions here are conceptual guides. Formal definitions, notation, propositions, and worked examples will be released in versioned technical notes and preprints.