Probabilistic Epistemic Dynamic Agentive Logic

2026-04-23

AI Summary

This study addresses the formal characterization of an agent’s probabilistic epistemic state concerning specification satisfaction in program verification. To this end, the paper introduces a novel probabilistic epistemic dynamic logic, termed PEDAL, which precisely models epistemic dynamics by endowing the set of program valuations in propositional dynamic logic (PDL) models with a probability measure. The main contributions include the first integration of probability measures into dynamic epistemic logic, the construction of a Hilbert-style axiomatization featuring infinitary inference rules, and strategies to mitigate the resulting proof-theoretic complexity. Furthermore, the work establishes a formal semantics and a corresponding axiomatic system for PEDAL and proves its soundness and strong completeness.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Machine Learning: Probabilistic Circuits and Graphical Models

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: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

I introduce PEDAL -- a probabilistic epistemic logic meant to capture, in propositional dynamic terms, the epistemic state of an agent engaged in checking whether a program meets its specification. Semantically, PEDAL is built `on top of' PDL and uses probability measures defined on the set of possible program valuations of an otherwise-specified PDL-model. A Hilbert system with one infinitary rule is provided and proved to be sound and complete. Near the end, I discuss possible ways to circumvent infinitary proof difficulties.

Problem

• probabilistic epistemic logic
• propositional dynamic logic
• program verification
• epistemic state
• probability measures

Innovation

• probabilistic epistemic logic
• propositional dynamic logic
• program verification
• Hilbert system
• probability measures