# Information-Guided Temporal Logic Inference with Prior Knowledge

arXiv: https://arxiv.org/abs/1811.08846 · HTML: https://mlsanity.com/paper/1811.08846/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2018.

## Built on by (most cited first, 13 of 13)

- [Learning Interpretable Temporal Properties from Positive Examples Only](https://mlsanity.com/paper/2209.02650/) (2022)
- [Learning Linear Temporal Properties from Noisy Data: A MaxSAT Approach](https://mlsanity.com/paper/2104.15083/) (2021)
- [Classification of Time-Series Data Using Boosted Decision Trees](https://mlsanity.com/paper/2110.00581/) (2021)
- [TLINet: Differentiable Neural Network Temporal Logic Inference](https://mlsanity.com/paper/2405.06670/) (2024)
- [Neural Network for Weighted Signal Temporal Logic](https://mlsanity.com/paper/2104.05435/) (2021)
- [Inferring Temporal Logic Properties from Data using Boosted Decision Trees](https://mlsanity.com/paper/2105.11508/) (2021)
- [Supervised Bayesian Specification Inference from Demonstrations](https://mlsanity.com/paper/2107.02912/) (2021)
- [On Generating Explanations for Reinforcement Learning Policies: An Empirical Study](https://mlsanity.com/paper/2309.16960/) (2023)
- [A Safe Preference Learning Approach for Personalization with Applications to Autonomous Vehicles](https://mlsanity.com/paper/2311.02099/) (2023)
- [Time-Incremental Learning from Data Using Temporal Logics](https://mlsanity.com/paper/2112.14300/) (2021)
- [Learning Probabilistic Temporal Safety Properties from Examples in Relational Domains](https://mlsanity.com/paper/2211.03461/) (2022)
- [Data-Driven Model Discrimination of Switched Nonlinear Systems with Temporal Logic Inference](https://mlsanity.com/paper/2306.09966/) (2023)
- [Class-Conditional Conformal Prediction for Signal Temporal Logic Inference with Many Classes](https://mlsanity.com/paper/2610.14352/) (2026)

## Abstract (arXiv)

This paper investigates the problem of inferring knowledge from data so that the inferred knowledge is interpretable and informative to humans who have prior knowledge. Given a dataset as a collection of system trajectories, we infer parametric linear temporal logic (pLTL) formulas that are informative and satisfied by the trajectories in the dataset with high probability. The informativeness of the inferred formula is measured by the information gain with respect to given prior knowledge represented by a prior probability distribution. We first present two algorithms to compute the information gain with a focus on two types of prior probability distributions: stationary probability distributions and probability distributions expressed by discrete time Markov chains. Then we provide a method to solve the inference problem for a subset of pLTL formulas with polynomial time complexity with respect to the number of Boolean connectives in the formula. We provide implementations of the proposed approach on explaining anomalous patterns, patterns changes and explaining the policies of Markov decision processes.