TAG ARCHIVE
formal-methods
4 MARIA OS blog articles tagged formal-methods, organized as a Bonginkan topic archive for search engines and LLM retrieval.
Judgment OS / Decision Intelligence OS
Core MARIA OS research on turning organizational judgment into executable decision systems.
Agentic Company Architecture
Research on human-agent organizations, delegation boundaries, role topology, and governed autonomy.
Responsibility Gates and AI Governance
Safety, accountability, fail-closed gates, auditability, and human-in-the-loop control for AI agents.
Multi-Agent Mathematics
Formal models for convergence, stability, game theory, graph dynamics, and multi-agent evaluation.
Evidence, RAG, and Knowledge Governance
Evidence bundles, retrieval architecture, Graph RAG, knowledge trust, and auditable reasoning pipelines.
Agentic R&D and Judgment Science
Research operations, simulation labs, judgment science, recursive improvement, and experimental AI governance.
Voice-Driven Agentic Avatars: A Recursive Self-Improvement Framework for Autonomous Intellectual Task Delegation
Formal convergence analysis, delegation-completeness theorems, and safety bounds for voice-mediated multi-agent governance systems
We present the Voice-Driven Agentic Avatar (VDAA) framework, a formal model of voice-mediated intellectual task delegation in multi-agent systems. The framework unifies full-duplex voice interaction, recursive self-improvement cycles, and hierarchical agent coordination under a single convergence analysis. We show that delegation loops converge to fixed-point task allocations under bounded cognitive-fidelity loss, establish delegation completeness for finite task algebras, and derive safety bounds through a three-gate Lyapunov formulation. Evaluation on MARIA VOICE reports 94.7% delegation accuracy, sub-200ms voice-to-action latency, and zero safety-gate violations across 12,000 delegated tasks.
Cognitive Science Foundations of Voice User Interface Design: An Attention Resource Allocation Model for Multimodal Dialogue
Integrating Wickens' multiple resource theory, Baddeley's working memory model, and information theory to formalize VUI design principles and validate them in the MARIA VOICE implementation
Voice user interface (VUI) design tends to rely on heuristics that do not adequately address the characteristics of auditory cognitive processing. This paper integrates Wickens' multiple resource theory, Baddeley's working memory model, and Shannon information theory to present a mathematical model of attention resource allocation in multimodal dialogue. We demonstrate the cognitive optimality of sentence-level streaming TTS, the theoretical basis for the 1.2-second debounce threshold, and the conditions under which barge-in suppression avoids resource conflict, providing a theoretical account of MARIA VOICE's design decisions.
Decision Intelligence Theory: A Unified Framework for Responsible AI Governance
Five axioms, four pillar equations, and five theorems that transform organizational judgment into executable decision systems
Decision Intelligence Theory formalizes decision-making as a control system, integrating evidence, conflict, responsibility, execution, and learning. This capstone article presents a unified mathematical framework — five axioms, four pillar equations, and five theorems — together with implementation mappings and internal cohort analyses across finance, healthcare, legal, and manufacturing.
A Formal Model of Responsibility Decomposition Points in Human-AI Decision Systems
Why responsibility is a computable threshold, not a philosophical debate - and how to implement it
Existing AI governance frameworks rely on qualitative guidelines to determine when human oversight is required. This paper formalizes responsibility decomposition as a quantitative threshold problem: we define a Responsibility Demand Function R(d) over decision nodes using five normalized factors - impact, uncertainty, externality, accountability, and novelty - and introduce a decomposition threshold τ that determines when human responsibility must be enforced. A dynamic equilibrium model captures temporal shifts driven by learning and contextual change. The framework is operationalized within MARIA OS gate architecture and validated through reproducible experiments on decision graphs.