Transition Grammar: Reconstructing AI Reasoning Systems via State Transitions

The Transition Grammar open-source project proposes modeling AI reasoning as a state transition system instead of the traditional output generation paradigm. Its core goal is to address issues of stability, interpretability, and completeness assumptions in existing reasoning systems. By formally defining the state space, transition operators, trajectories, and goal conditions of the reasoning process, this framework provides a foundation for building more controllable and auditable reasoning systems, emphasizing features like stability (deterministic reasoning), modular operator design (composable verification), and elegant handling of incompleteness (acknowledging "I don't know").

The reasoning of current large language models relies on the autoregressive generation paradigm, which has three major structural limitations:

1. Stability Issue: The randomness of autoregressive generation leads to different results for the same problem, affecting applications in reliable scenarios (e.g., medical diagnosis);
2. Opaque Process: The generated "thinking process" may not align with internal computations, leading to "hallucinatory reasoning" and reduced interpretability;
3. Completeness Assumption: Models always force an output even when beyond their capabilities, easily leading to errors.

Transition Grammar defines reasoning as a state transition system, formalized as a quadruple (S, O, T, G):

• S: State space, including cognitive snapshots like propositions, hypotheses, and goals;
• O: Set of transition operators, defining valid state transitions;
• T: Transition trajectory, recording the reasoning process;
• G: Goal conditions, defining the state of a successful conclusion. This framework separates reasoning structure from content, providing clear entry points for system analysis, verification, and optimization.

Key features of the framework include:

1. Stability: Operators are deterministic functions without random sampling, ensuring consistent reasoning paths under the same initial state, supporting explicit branch exploration and backtracking;
2. Operator Selection: Modular design—operators are basic reasoning units (e.g., decomposition, integration, matching) with composable, verifiable, and extensible properties. The project provides a basic operator library;
3. Elegant Incompleteness: When the goal cannot be reached, it enters a pause state carrying meta-information (unsolved subproblems, information to be supplemented), supporting incremental reasoning.

Transition Grammar adopts a neuro-symbolic hybrid architecture:

• Neural networks handle perceptual tasks like pattern recognition and semantic understanding;
• The state transition framework controls the reasoning structure; Integration methods include: implementing operators with neural networks (to handle complex semantics), using neural networks as external knowledge sources (query interfaces for information), balancing flexibility and interpretability.

The framework is suitable for the following scenarios:

• Structured Decision Support: Fields requiring interpretability and auditability, such as medical diagnosis and financial risk control;
• Educational Tutoring: Explicitly displaying reasoning steps to help students understand the thinking process;
• Scientific Hypothesis Generation: Systematically exploring the hypothesis space and evaluating evidence support;
• Formal Verification: Automated proof in scenarios like software and protocols.

The current framework faces challenges:

1. Expressive Power: Difficulty capturing human reasoning like intuitive leaps and creative associations;
2. Computational Complexity: State space search is prone to combinatorial explosion;
3. Knowledge Acquisition: Automatic extraction of structured knowledge and operator definitions;
4. User Interaction: Need to design intuitive interfaces to display the reasoning process. Future directions include enriching the operator library, automatic operator learning, efficient search algorithms, optimizing interactive tools, and scenario validation.