Attributing Distributed Responsibility in Stit Logic

One important function of logics of agency (Stit Logic, ATL, CL, Dynamic Logic) is to assess the validity of arguments whereby responsibility is attributed to, or denied by, individuals and groups. Indeed, the vocabulary and computational properties of such logic allow us to express and reason on what agents did, or what empowered them to do (either following a strategy as in ATL or not). It is clear that this kind of reasoning is indispensable when we want to attribute or distribute responsibility to agents, as when we want to ascertain that some agents were not responsible of the events into account: if the group constituted by two persons did not or even could not for some reasons blow a hospital, then they should not be charged for blowing the hospital. Agency and the formal framework for it then appear to be important for the implementation of a rigourous reasoning on responsibility in (or of) groups. Various developments have been carried over from a pure logic of agency to frameworks where agency interacts with other notions. Focusing on Stit Logic, the addition of knowledge (Broersen [4] and [5]) and intention (Broersen [6]) operators allows for the expression of statements such as that one did something (un)knowingly or (un)intentionally. Here we make a further step in this direction, by introducing expressions stating that an individual or group did not do more than so-and-so. For instance, if responsibility is attributed to a group for the robbing of a bank, then one member of the group may state that all he did was to drive the others there and back. The setting we propose will enable us to express the conditions for attributing or distributing responsibility. In Stit Logic any set of individuals counts as a group, and the combination of their individual actions counts as their group action. This means that the group of you and some bank robber can be attributed responsibility for the combination of watering the plants and robbing a bank, although all that you did was water the plants. We shall call “agents” the individuals and “coalitions” the groups of agents, thus following standard terminology in logics of agency. If we aim at expressing the fact that an agent did something while another in fact did not, it is necessary to expand the basic formal framework of stit logic.