On the Axiomatization of Elgesem’s Logic of Agency and Ability

Modal logic of agency is a traditional research field in philosophical logic. Roughly speaking, the approach adopts the general policy to abstract from making explicit state changes and from considering the temporal dimension in describing actions. In fact, actions are simply taken to be relationships between agents and states of affairs. Thus, the conceptual qualification of these relations is made by using suitable modal operators to represent, for example, that an agent “brings it about” or “sees to it” that A, or that such agent is “able” to realise A, or again that she “attempts” to achieve it. It is well known that modal logic of agency has a number of drawbacks. As recently summarised in [24], the main limit of this approach, as found in the literature, is that it is “too abstract”. For example, it is not usually captured the difference between the modal qualifications “sees to it” and “brings it about”. Both expressions are in general represented by a single modal operator, despite the fact that the former exhibits a clear intentional character, whereas the latter may refer as well to unintentional actions [11]. Secondly, for the purpose of analysing the structure of multi-agent contexts it is crucial to distinguish between direct actions and indirect actions. This is necessary, for example, to account for the notions of influence and control of an agent over other agents [14, 15, 19, 20]. While these problems may be, or have been, solved by providing suitable integrations and new operators within the same paradigm of modal logic of agency, a last drawback is inherent in the paradigm as such. In fact, “sometimes it is essential to be able to refer to the means by which an agent brings about a state of affairs”, as for example by referring to specific actions performed to achieve a goal [24]. As it is well-known, this shows that modal logic of agency is less expressive than other formal theories of action, such as dynamic logics. On the other hand, this last limit is also an advantage. Although the abstractness of modal logic of agency does not make the language very expressive in itself, it allows flexibility for the easy combination of agency with a number of other concepts, such as powers,