# Statistical Model Checking for Probabilistic Temporal Epistemic Logics

### Yenda Ramesh, M. Rao

#### 2022

#### Abstract

Interpreted Systems and epistemic temporal logics have been employed extensively to study the notion of knowledge in Multi-Agent Systems. New model checking algorithms, as well as adaptations of existing algorithms to this setting have been reported. For the most part, these algorithms have focused on exhaustive state space exploration based approaches. While these approaches yield accurate results to model checking queries, they are often expensive for realistic scenarios. So much so that, many of the applications studied in academic literature deal with small state spaces. In order to scale to real life multi-agent systems with large state spaces, an alternative to exhaustive exploration based techniques is needed. Statistical Model Checking was proposed to alleviate this problem when model checking stochastic systems against temporal logic queries. In this paper, we extend this technique to epistemic temporal logics. The first version of the approach, which we call the vanilla approach, would be to simply generate Monte Carlo samples of the runs of the system and evaluate the query on them. The advantage that SMC is expected to bring is greatly diminished due to the knowledge operator in such systems of logic. For large systems, this would entail an exhaustive exploration of epistemically accessible global states. Our major contribution is to introduce a sampling based approach for the knowledge operator as well. We show that this results in significant performance gains at the expense of a marginal loss in accuracy (1-2% in experimental results) for most epistemic operators. Specifically, we show evidence of a dramatic improvement in time complexity for large Multi-Agent Systems. We substantiate the effectiveness of the approach through case studies that involve a large number of agents.

Download#### Paper Citation

#### in Harvard Style

Ramesh Y. and Rao M. (2022). **Statistical Model Checking for Probabilistic Temporal Epistemic Logics**. In *Proceedings of the 14th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,* ISBN 978-989-758-547-0, pages 53-63. DOI: 10.5220/0010847900003116

#### in Bibtex Style

@conference{icaart22,

author={Yenda Ramesh and M. Rao},

title={Statistical Model Checking for Probabilistic Temporal Epistemic Logics},

booktitle={Proceedings of the 14th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},

year={2022},

pages={53-63},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010847900003116},

isbn={978-989-758-547-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 14th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,

TI - Statistical Model Checking for Probabilistic Temporal Epistemic Logics

SN - 978-989-758-547-0

AU - Ramesh Y.

AU - Rao M.

PY - 2022

SP - 53

EP - 63

DO - 10.5220/0010847900003116