CAREER: Theoretical Foundations for Problem Space Representation and Reasoning in Systems Engineering

This Faculty Early Career Development (CAREER) award supports fundamental research focused on how engineers formulate, analyze, and validate engineering problem spaces by creating a new theoretical foundation that integrates rigorous logic-based methods with real-world engineering practice. Modern society depends on large-scale, complex engineering systems like communication satellites, aircraft, rockets, and critical infrastructure.

Developing these systems requires engineers to correctly understand and represent the "problem space", that is, the fundamental questions about what the system should do and how it should interact with its environment. If these early problem formulations are incomplete or inconsistent, costly design errors can arise down the road, affecting reliability, safety, and mission success.

By ensuring that needs, requirements, and system functions are represented in a mathematically sound, complete, and consistent manner, this research intends to reduce costly rework, enhance system safety, and improve performance. This effort intends to enable national leadership in cutting-edge engineering, promote scientific progress, and advance societal welfare by ensuring that future large-scale systems are designed with mathematical rigor from the earliest stages.

The educational component of the project is focused on transforming the way students learn about and approach engineering problem formulation, equipping the next generation of engineers with advanced formal reasoning skills.

The intellectual merit of this CAREER project is on developing theoretical foundations for representing and reasoning about engineering problem spaces through the integration of Modal Preference Logic, Systems Theory, and Set Theory. The research establishes formal definitions, axioms, and theorems for analyzing the consistency, completeness, and validity of problem space elements and their transformations.

Automated reasoning tools will be developed to support practical application. The methodology will be validated through formal mathematical proofs and real-world case studies of space systems at National Aeronautics and Space Administration (NASA) Marshal Space Flight Center’s Advanced Concepts Office. Scientific contributions include a unified logical framework for representing diverse problem space elements, formal criteria for assessing problem formulation quality, and theoretical foundations for verification and validation integrated directly into the problem formulation process.

The framework will be implemented through an ontology that enables automated reasoning about complex system specifications while maintaining mathematical rigor. The educational component of this project integrates these formal methods into the engineering curriculum through advanced undergraduate and graduate courses, ensuring that students gain hands-on experience with rigorous logic, problem formulation, and automated reasoning.

Partnerships with the Alabama Space Grant Consortium will expose high-school and university students to cutting-edge methods and tools, broadening participation in engineering fields and preparing a workforce that can confidently meet the complex engineering challenges of tomorrow. By linking cutting-edge research with classroom teaching, and educational outreach, the project provides a comprehensive solution that supports both the scientific community and the broader national interest in reliable, efficient, and innovative engineering systems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.