# Explaining Optimal Trajectories

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Rules and Reasoning (RuleML+RR 2023)

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## Abstract

We propose a definition of common explanation for the label shared by a group of observations described as first order interpretations, and provide algorithms to enumerate minimal common explanations. This was motivated by explaining how performing some action, for instance a card played during a card game play, results in winning a maximum total reward at the end of the trajectory. As there are various ways to reach this reward, each associated to a group of trajectories, we propose to first build groups of trajectories and then build minimal common explanations for each group. The whole method is illustrated on a simplified Bridge game.

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## Notes

1. 1.

Using the ILP system cLear, developed by NukkAI.

2. 2.

While most predicates are self-explanatory some are not. $$willTakeTrickWith (12, north ,T)$$ says that at time T and by playing 12 which is the highest card on the board or in hands of players that yet have to play in the current trick, North will win the trick. $$nbThreats (2,Player,0,[7,7])$$ says that at time $$t_7$$ card 2 of $$Player$$ has no threats by cards from its opponents. It also says that such threatening cards exists in $$t_6$$.

3. 3.

If possible the opponent plays a card higher than the last card played in the trick.

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## Acknowledgements

We thank Dr Junkang Li who wrote the program that solves the MDP and Dr Dominique Bouthinon for helping us to apply the ILP program cLear for the simplified Bridge game. M. Kazi Aoual is partially supported by ANRT through a CIFRE agreement.

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Correspondence to Henry Soldano .

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### Cite this paper

Rouveirol, C., Kazi Aoual, M., Soldano, H., Ventos, V. (2023). Explaining Optimal Trajectories. In: Fensel, A., Ozaki, A., Roman, D., Soylu, A. (eds) Rules and Reasoning. RuleML+RR 2023. Lecture Notes in Computer Science, vol 14244. Springer, Cham. https://doi.org/10.1007/978-3-031-45072-3_15

• DOI: https://doi.org/10.1007/978-3-031-45072-3_15

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• Publisher Name: Springer, Cham

• Print ISBN: 978-3-031-45071-6

• Online ISBN: 978-3-031-45072-3

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