Abstract Coalition logic is an important logic in the logical studies of strategic reasoning, whose models are concurrent game models. In this paper, we first systematically discuss three assumptions of concurrent game models and argue that they are too strong. The first is seriality, i.e. every coalition always has an available joint action. The second is the independence of agents, i.e. 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, i.e. 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 that do not have the three assumptions and show its completeness. This logic seems minimal for reasoning about coalitional powers.

Duties and powers are two fundamental notions in private law. In this work, we provide our conception of duties and powers and present a logic for reasoning about them. We treat duties as agents' obligations towards others to perform actions. We think that powers are agents' legal abilities, conferred by law, to change legal positions between agents. How to exercise powers is also specified by law. Many factors, including the exercise of powers, fulfillment of duties, violation of duties, and factual changes in the world, can change duties. The ontic level of the logic is a multi-agent dynamic logic, where agents have abilities to change atomic facts. At its normative level, agents have duties towards others to change atomic facts, and have powers to change duties by changing atomic facts. When agents behave, the ontic and normative aspects of the world change accordingly. The implications of the formalization are studied extensively.

Abstract Conflicts between legal norms are common in reality. In many legislations, legal conflicts between norms are resolved by applying ordered principles. This work presents a formalization of the conflict resolution mechanism and introduces action legal logic ($\textsf{ALL}$) to reason about the normative consequences of possibly conflicting legal systems. The semantics of $\textsf{ALL}$ is explicitly based on legal systems consisting of norms and ordered principles. Legal systems specify the legal status of transitions in transition systems and the language of $\textsf{ALL}$ describes the legal status of paths in transition systems. The formalization is used to study abstract revisions of legal systems. The expressivity of $\textsf{ALL}$ is studied and its completeness is proved.

This paper presents a formalization of refraining from actions and a deontic logic based on a process logic. The notion of refraining is needed to handle obligated actions. To refrain to do an action is to do something else. The process logic used is a mix of dynamic logic and temporal logic: actions in it are interpreted as sets of paths and temporal formulas describe the process of performing actions. The deontic logic has a temporal propositional constant saying that a bad thing will be done in the next moment. Normative properties of actions can be defined according to what happens in the process of performing actions.

We aim to present a dynamic deontic logic. This logic is an extension of Boolean Modal Logic in both language and semantics. This logic's language has a deontic operator, applied to actions, and two dynamic operators. In the logic's semantics, the deontic relation is defined on the set of finite sequences of states, called histories, and formulas are evaluated at the histories. The deontic operator describes obligations and freedoms of agents, whereas the two dynamic operators correspond to giving orders and permissions, which change agents' obligations and freedoms in different ways.