A formal theory on problem space as a semantic world model in systems engineering

Classic problem-space theory models problem solving as a navigation through a structured space of states, operators, goals, and constraints. Systems Engineering (SE) employs analogous constructs (functional analysis, operational analysis, scenarios, trade studies), yet still lacks a rigorous systems-theoretic representation of the problem space itself. In current practice, reasoning often proceeds directly from stakeholder goals to prescriptive artifacts. This makes foundational assumptions about the operational environment, admissible interactions, and contextual conditions implicit or prematurely embedded in architectures or requirements. This paper addresses that gap by formalizing the problem space as an explicit semantic world model containing theoretical constructs that are defined prior to requirements and solution commitments. These constructs along with the developed axioms, theorems and corollary establish a rigorous criterion for unambiguous boundary semantics, context-dependent interaction traceability to successful stakeholder goal satisfaction, and sufficiency of problem-space specification over which disciplined reasoning can occur independent of solution design. It offers a clear distinction between what is true of the problem domain and what is chosen as a solution. The paper concludes by discussing the significance of the theory on practitioners and provides a dialogue-based hypothetical case study between a stakeholder and an engineer, demonstrating how the theory guides problem framing before designing any prescriptive artifacts.