Learning Probabilisitic Temporal Logic Specifications for Stochastic Systems

Rajarshi Roy, Yash Pote, David Parker, Marta Kwiatkowska

Keywords: Temporal Logic, Symbolic Learning, Stochastic Systems

TL;DR: This paper introduces a learning framework for probabilistic specifications in temporal logics for stochastic systems

Abstract: There has been substantial progress in the inference of formal behavioural specifications from sample trajectories, for example, using Linear Temporal Logic (LTL). However, these techniques can not handle specifications that correctly characterise systems with stochastic behaviour, which occur commonly in reinforcement learning and formal verification. We consider the passive learning problem of inferring a Boolean combination of probabilistic LTL (PLTL) formulas from a set of Markov chains, classified as either positive or negative. We propose a novel learning algorithm that infers concise PLTL specifications, leveraging grammar-based enumeration, search heuristics, probabilistic model checking and Boolean set-cover procedures. We demonstrate the effectiveness of our algorithm in two use cases: learning from policies induced by RL algorithms and learning from variants of a probabilistic model. In both cases, our method automatically and efficiently extracts PLTL specifications that succinctly characterise the temporal differences between the policies or model variants.

Paper Type: New Full Paper

Venue For Previously Published Paper: IJCAI 2025

Submission Number: 20