Some Examples Formulated in a ‘Seeing to It That’ Logic: Illustrations, Observations, Problems

Abstract

The chapter presents a series of small examples and discusses how they might be formulated in a 'seeing to it that' logic. The aim is to identify some of the strengths and weaknesses of this approach to the treatment of action. The examples have a very simple temporal structure. An element of indeterminism is introduced by uncertainty in the environment and by the actions of other agents. The formalism chosen combines a logic of agency with a transition-based account of action: the semantical framework is a labelled transition system extended with a component that picks out the contribution of a particular agent in a given transition. Although this is not a species of the stit logics associated with Nuel Belnap and colleagues, it does have many features in common. Most of the points that arise apply equally to stit logics. They are, in summary: whether explicit names for actions can be avoided, the need for weaker forms of responsibility or 'bringing it about' than are captured by stit and similar logics, some common patterns in which one agent's actions constrain or determine the actions of another, and some comments on the effects that level of detail, or 'granularity', of a representation can have on the properties we wish to examine.

Connecting Actions and States in Deontic Logic

“…This is because we intended to stay on the level of deontic operators and restrict our research here to understanding the mutual dependency between a-norms and s-norms. The PDL-like and STIT-like operators can be easily added to our framework in the similar way as shown for instance by Sergot in [13,14]. The key point of our and Sergot's approaches (Sergot's and our models are very similar) is that we treat the models as more fundamental for analyses of deontic issues.…”

“…The set LEG a s (w), defined as a powerset, 14 has the properties analogous to (1) and (2) as it is expected for strong permission; cf. [12,18].…”

“…Thus, it may happen that on the one hand, we have an indeterministic execution of an action, e.g. w 1 , w 2 , e ∈ Step and w 1 , w 3 , e ∈ Step (w 2 = w 3 ), and, on the other hand, that the same transition is a result of the execution of two different 3 Indeed, an action frame can be seen as a labelled transition system as described in [14]. In the action model we do not really take advantage of the information about the final state of the transitions.…”

“…We do not introduce agents into our formalism explicitly, but we tacitly assume that actions are carried out by them. We can extend the system by incorporating agents into names of basic actions in the way that is analogical to [13,14], where agents' names are parts of transition atoms. That would enable us to extend the presented solutions in a multi-agent system direction.…”

“…There are some works that tackle this problem such as [6,19] and recently [7], but we are not fully pleased with those solutions mostly because of the fact that they do not really separate the deontic properties of actions from the properties of states. An approach closer to ours is presented in [4,[13][14][15], where a two-sorted propositional language is used to deal separately with the properties of states and the properties of actions. However, the deontic properties of actions and the properties of states are connected only very loosely in those works.…”