Reasoning Systems as Structured Processes: Foundations, Failures, and Formal Criteria

2025-08-03

AI Summary

Existing inference systems lack cross-domain comparability and a principled foundation for failure analysis. Method: This paper proposes a universal, algorithm-agnostic formal framework that models inference systems as structured tuples comprising phenomena, explanation spaces, inference/generation mappings, and principled foundations. It innovatively incorporates dynamic behavioral modeling—such as iterative optimization and principle evolution—and an endogenous failure taxonomy covering contradiction, incompleteness, non-convergence, and related patterns. Contribution/Results: The framework unifies logical, algorithmic, and learning-based inference under a common formalism; rigorously defines core evaluation criteria—including coherence, reliability, and completeness—and provides a foundational basis for theoretical comparison, robustness analysis, and adaptive design of inference architectures. It enables systematic diagnosis of inference failures and supports principled engineering of next-generation reasoning systems.

Technology Category

• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space, inference and generation maps, and a principle base. The formulation accommodates logical, algorithmic, and learning-based reasoning processes within a unified structural schema, while remaining agnostic to any specific reasoning algorithm or logic system. We survey basic internal criteria--including coherence, soundness, and completeness-and catalog typical failure modes such as contradiction, incompleteness, and non-convergence. The framework also admits dynamic behaviors like iterative refinement and principle evolution. The goal of this work is to establish a foundational structure for representing and comparing reasoning systems, particularly in contexts where internal failure, adaptation, or fragmentation may arise. No specific solution architecture is proposed; instead, we aim to support future theoretical and practical investigations into reasoning under structural constraint.

Problem

• Develop a formal framework for analyzing reasoning systems
• Model reasoning systems with structured components and criteria
• Identify failure modes and dynamic behaviors in reasoning processes

Innovation

• General formal framework for reasoning systems
• Unified structural schema for reasoning processes
• Foundational structure for comparing reasoning systems