Learning Probabilistic Temporal Logic Specifications for Stochastic Systems

TL;DR

This paper introduces a new algorithm for inferring concise probabilistic temporal logic specifications from stochastic system data, addressing the limitations of existing methods for systems with inherent randomness.

Contribution

The paper presents a novel learning algorithm that infers probabilistic LTL formulas using grammar-based enumeration, heuristics, model checking, and set-cover techniques, specifically for stochastic systems.

Findings

Successfully infers concise PLTL specifications from Markov chains.

Effectively characterizes temporal differences in policies and model variants.

Automates extraction of probabilistic temporal logic from stochastic data.

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 cannot 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.