Indirect actions and authority relations in STIT and DPL

The article investigates the notion of an authority relation between agents from two perspectives. Its first part argues that the existence of an authority relation between agents, with respect to some state of affairs, means that an agent who is in authority has an ability to command to act in order to see to it that such state of affairs is true. A command of that kind is modelled in NEXT-semantics. Here an impact of one agent on another is pictured as a composition of accessibility relations between the worlds. A case of an embedded authority relation and a case of presupposed conditions are investigated. The second part of the article argues that an authority relation between agents, with respect to some state of affairs, exists due to a personal and immediate ability of an agent, who is in authority, to make that state of affairs true. Here an authority relation is interpreted on process graphs as a transitive move to the third world from the first one (where an agent who is in authority acts) via the second world (where an agent who is under authority acts) or as an ability of one agent to use others as a proxy for his or her actions. Such an ability is modelled for three agents by means of a special relation that can distinguish equivalent classes on process graphs. Finally, the article introduces some semantic ideas which are to make further synthesis of the logic of action and PDL fruitful.

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