A minimal coalition logic

Coalition Logic is an important logic in logical studies of strategic reasoning, whose models are concurrent game models. In this paper, first, we systematically discuss three assumptions of concurrent game models and argue that they are too strong. The first is seriality; that is, every coalition always has an available joint action. The second is the independence of agents; that is, the merge of two available joint actions of two disjoint coalitions is always an available joint action of the union of the two coalitions. The third is determinism; that is, all available joint actions of the grand coalition always have a unique outcome. Second, we present a coalition logic based on general concurrent game models which do not have the three assumptions and show its completeness. This logic seems minimal for reasoning about coalitional powers.