Instrumentalization of Norm-regulated Transition System Situations

Abstract

Abstract. An approach to normative systems in the context of multiagent systems (MAS) modeled as transition systems, in which actions are associated with transitions between different system states, is presented. The approach is based on relating the permission or prohibition of actions to the permission or prohibition of different types of state transitions with respect to some condition d on a number of agents x1, ..., xν in a state. It introduces the notion of a norm-regulated transition system situation, which is intended to represent a single step in the run of a (norm-regulated) transition system. The normative framework uses an algebraic representation of conditional norms and is based on a systematic exploration of the possible types of state transitions with respect to d(x1, ..., xν ). A general-level Java/Prolog framework for norm-regulated transition system situations has been developed, and this implementation together with a simple example system is presented and discussed.

Normative positions in multi-agent systems

“…It might be fruitful to develop a theory of normative positions based on some variant of stit theory or the operators suggested by Governatori et al, but these lines of thought are not further developed here; for the purposes of this paper, Kanger's simplistic approach will be a sufficient basis. The notion of a norm-regulated transition system situation was originally presented in [13]. A transition system situation is intended to represent, for example, a 'snapshot' of a labelled transition system (LTS) in which each transition fulfills these criteria.…”

“…This work may serve as a first step towards such a typology, by investigating how to apply the theory of one-agent normative positions in the context of a class of transition systems, in which transitions are deterministic and associated with a single agent performing an act. To study this class of systems, the notion of norm-regulated transition system situations [13,14] will be employed. Here, the permission or prohibition of actions is connected to the permission or prohibition of different types (with respect to some condition on a number of agents in a state) of state transitions.…”

Offline Evolution of Normative Systems

“…Note that, as regards the ground ( = ∧Lap 9 ), one of ( = ∧Lap 9 ), P k0 Lap 9 and ( = ∧Lap 9 ), P k1 Lap 6 is redundant (since the only conditions that can 8 The 'move operator' M1 identifies the agent to which the normative condition applies with the acting agent and with the first agent in the argument sequence Xν . See for example (Hjelmblom, 2013) for an explanation. In the following, M1 is omitted to facilitate reading.…”

“…In the following, we assume that norms always apply to the moving agent x in a situation x, s , in order to facilitate the presentation. A norm in N is represented by an ordered pair g, c , where the (descriptive) condition g on a situation x, s is the ground of the norm and the (normative) 3 In (Hjelmblom, 2013) such a tuple is called a transition system situation. 4 In the special case when the sequence of agents is empty, i.e.…”

“…(Odelstad and Boman, 2004, p. 146). condition c on x, s is its consequence; see, e.g., (Odelstad and Boman, 2004). We first define a set of 'transition type operators' C a k , based on Table 2 in (Hjelmblom, 2014a), and a set of corresponding 'transition type prohibition operators' P k , k ∈ {1, 2Λ, 2Ω, 4Λ, 4Ω, 5, 6Λ, 6Ω, 7}, such that P k d(X ν ; x, s) is intended to mean that if C a k d(X ν ; x, s) holds, then a is prohibited for x in x, s .…”