The paper introduces the Truth Maintenance System (TMS), a subsystem designed to manage and revise beliefs in reasoning programs. The TMS records and maintains reasons for program beliefs, enabling the construction of explanations and guiding the course of action. Key aspects include: 1. **Representations and Structure**: The TMS uses nodes to represent beliefs and justifications to represent reasons for beliefs. 2. **Truth Maintenance Mechanisms**: The TMS employs non-monotonic justifications, such as support-list (SL) and conditional-proof (CP) justifications, to handle changes in beliefs. 3. **Dependency-Directed Backtracking**: This mechanism helps resolve inconsistencies by tracing the dependencies of conflicting beliefs and retracting assumptions. 4. **Summarizing Arguments**: Techniques are described to summarize arguments and beliefs. 5. **Dialectical Arguments**: The TMS can organize problem solvers into modules that engage in dialectical reasoning. 6. **Models of Other's Beliefs**: The TMS can revise models of the belief systems of others. 7. **Assumptions and Control**: The TMS handles default assumptions, sequences of alternatives, and equivalence class representatives to manage control in reasoning processes. The paper emphasizes the need for problem solvers to choose between alternative systems of beliefs and outlines mechanisms for guiding these choices. The research was conducted at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology and supported by various grants from the Department of Defense and NSF.The paper introduces the Truth Maintenance System (TMS), a subsystem designed to manage and revise beliefs in reasoning programs. The TMS records and maintains reasons for program beliefs, enabling the construction of explanations and guiding the course of action. Key aspects include: 1. **Representations and Structure**: The TMS uses nodes to represent beliefs and justifications to represent reasons for beliefs. 2. **Truth Maintenance Mechanisms**: The TMS employs non-monotonic justifications, such as support-list (SL) and conditional-proof (CP) justifications, to handle changes in beliefs. 3. **Dependency-Directed Backtracking**: This mechanism helps resolve inconsistencies by tracing the dependencies of conflicting beliefs and retracting assumptions. 4. **Summarizing Arguments**: Techniques are described to summarize arguments and beliefs. 5. **Dialectical Arguments**: The TMS can organize problem solvers into modules that engage in dialectical reasoning. 6. **Models of Other's Beliefs**: The TMS can revise models of the belief systems of others. 7. **Assumptions and Control**: The TMS handles default assumptions, sequences of alternatives, and equivalence class representatives to manage control in reasoning processes. The paper emphasizes the need for problem solvers to choose between alternative systems of beliefs and outlines mechanisms for guiding these choices. The research was conducted at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology and supported by various grants from the Department of Defense and NSF.