Bridging LTLf Inference to GNN Inference for Learning LTLf Formulae

Abstract

Learning linear temporal logic on finite traces (LTLf) formulae aims to learn a target formula that characterizes the high-level behavior of a system from observation traces in planning. Existing approaches to learning LTLf formulae, however, can hardly learn accurate LTLf formulae from noisy data. It is challenging to design an efficient search mechanism in the large search space in form of arbitrary LTLf formulae while alleviating the wrong search bias resulting from noisy data. In this paper, we tackle this problem by bridging LTLf inference to GNN inference. Our key theoretical contribution is showing that GNN inference can simulate LTLf inference to distinguish traces. Based on our theoretical result, we design a GNN-based approach, GLTLf, which combines GNN inference and parameter interpretation to seek the target formula in the large search space. Thanks to the non-deterministic learning process of GNNs, GLTLf is able to cope with noise. We evaluate GLTLf on various datasets with noise. Our experimental results confirm the effectiveness of GNN inference in learning LTLf formulae and show that GLTLf is superior to the state-of-the-art approaches.

End-to-End Learning of LTLf Formulae by Faithful LTLf Encoding

“…Gaglione et al (2021) proposed a MaxSAT-based approach to tolerate imperfect data, but the scalability is limited by the computational complexity of the MaxSAT solver. The work (Luo et al 2022) is the closest to this work. Based on a theoretical result that the graph neural network (GNN) inference is able to simulate the LTL f inference in checking if a trace is satisfied, Luo et al (2022) first trained a GNN classifier for the trace satisfiability problem and then interpreted LTL f formulae from the model parameters.…”

“…Formulae with tree structures widely exist in data mining and knowledge management, e.g., linear temporal logic (LTL) (Luo et al 2022) and regular expression (Ye et al 2023). Therefore, it is important to automatically discover the underlying tree structured formulae from large amounts of data.…”

“…To tackle the above challenges, some approaches (Camacho and McIlraith 2019; Luo et al 2022) modeled the relation between syntax and semantics by introducing an intermediate representation, but they need to pay additional costs from learning the over-expressive intermediate representation.…”

“…Following the assessment of the state-of-the-art (SOTA) approach (Luo et al 2022), we evaluate TLTLf across datasets with and without imperfect data. Experimental results show that TLTLf achieves SOTA performance and improves the accuracy by up to 7% compared with the SOTA approach.…”

“…Besides, the LTL f formula learnt by TLTLf is highly faithful to the network from which it is extracted, giving the same satisfiability results over 95% traces. Following the work (Kim et al 2019;Luo et al 2022), we also evaluate TLTLf on imperfect data generated by assigning incorrect labels to a subset of the original data. Results demonstrate that TLTLf still outperforms other approaches on imperfect data.…”