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arXiv · 2505.06960

First-Order Coalition Logic

Davide Catta·Rustam Galimullin·Aniello Murano
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Abstract

We introduce First-Order Coalition Logic ($\mathsf{FOCL}$), which combines key intuitions behind Coalition Logic ($\mathsf{CL}$) and Strategy Logic ($\mathsf{SL}$). Specifically, $\mathsf{FOCL}$ allows for arbitrary quantification over actions of agents. $\mathsf{FOCL}$ is interesting for several reasons. First, we show that $\mathsf{FOCL}$ is strictly more expressive than existing coalition logics. Second, we provide a sound and complete axiomatisation of $\mathsf{FOCL}$, which, to the best of our knowledge, is the first axiomatisation of any variant of $\mathsf{SL}$ in the literature. Finally, while discussing the satisfiability problem for $\mathsf{FOCL}$, we reopen the question of the recursive axiomatisability of $\mathsf{SL}$.

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Davide Catta, Rustam Galimullin, Aniello Murano. 2025-05-11. First-Order Coalition Logic. https://arxiv.org/abs/2505.06960

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