Programming and Reasoning in Partially Observable Probabilistic Environments

2025-06-16

AI Summary

To address the challenges of modeling and verifying programs in partially observable stochastic environments, this paper introduces pBLIMP—the first belief programming language supporting symbolic belief representation, probabilistic belief updates, and conditional decision-making. Methodologically, pBLIMP (1) establishes a symbolic belief state representation based on probability distributions, equipped with rigorous operational semantics; (2) devises the first weakest-precondition (wp) calculus framework tailored for partially observable settings, enabling sound reasoning about unbounded loops with invariants; and (3) formally proves the soundness and completeness of this wp-calculus. The language supports precise verification of state estimation, observation fusion, and probabilistic control flow. By unifying symbolic reasoning over beliefs with compositional program logic, pBLIMP lays a foundational theoretical basis for the design and formal verification of probabilistic belief programming languages.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Knowledge Representation and Reasoning: Reasoning with Beliefs
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

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

Abstract

Probabilistic partial observability is a phenomenon occuring when computer systems are deployed in environments that behave probabilistically and whose exact state cannot be fully observed. In this work, we lay the theoretical groundwork for a probabilistic belief programming language pBLIMP, which maintains a probability distribution over the possible environment states, called a belief state. pBLIMP has language features to symbolically model the behavior of and interaction with the partially observable environment and to condition the belief state based on explicit observations. In particular, pBLIMP programs can perform state estimation and base their decisions (i.e. the control flow) on the likelihood that certain conditions hold in the current state. Furthermore, pBLIMP features unbounded loops, which sets it apart from many other probabilistic programming languages. For reasoning about pBLIMP programs and the situations they model, we present a weakest-precondition-style calculus (wp) that is capable of reasoning about unbounded loops. Soundness of our wp calculus is proven with respect to an operational semantics. We further demonstrate how our wp calculus reasons about (unbounded) loops with loop invariants.

Problem

• Develop probabilistic belief language for partially observable environments
• Enable state estimation and decision-making under uncertainty
• Provide reasoning calculus for unbounded loops in probabilistic programs

Innovation

• Probabilistic belief programming language pBLIMP
• Weakest-precondition-style calculus for reasoning
• Unbounded loops with loop invariants support