We propose a computationally oriented non-monotonic multi-modal logic arising from the combination of temporalised agency and temporalised normative positions. We argue about the defeasible nature of these notions and then we show how to represent and reason with them in the setting of Defeasible Logic. An increasing number of works on agents assume that in artificial societies normative concepts may play a decisive role, allowing for the flexible co-ordination of autonomous agents [5, 20, 15] . In particular, it seems crucial to model organisations of agents in terms of policy-based normative systems; accordingly an organisation should be characterised by specifying the normative positions relevant to design its structure. These positions include duties, permissions, but also powers, as for instance powers of creating further normative positions on the head of other agents. In this paper we will develop a formal machinery to account for several fundamental concepts that are required to model policy-based normative systems. These concepts will be embedded in a nonmonotonic and computationally-oriented framework based on Defeasible Logic (DL). From the conceptual standpoint, it is well known that the basic deontic qualifications (obligatory, forbidden, permitted and facultative) are not sufficient to capture all fundamental normative notions, such as the concepts of rights and power. For this reason, we will first provide an account in DL of the notion of other-directed obligation [14] to express, e.g., the first Hohfeldian set of fundamental concepts: duty, right, noright, and privilege. Second, we shall focus on different kinds of normative conditionals. This will enable us to characterise also the idea of normative power and articulate many potestative concepts such as the second Hohfeldian set of concepts: power, liability (or, subjection, to avoid confusion with the notion of liability, as used in tort law), disability, and immunity. In general, we shall see how the analysis of normative conditionality and normative positions has to include temporal aspects in order to capture a number of nuances in the perspective of framing a fine-grained classification of such concepts. In fact, normative determinations take place along the axis of time: Normative preconditions hold or happen in certain temporally characterised occasions, and consequently their effects too hold or happen within temporal bounds. In providing an analysis of normative conditionality, we cannot refrain from introducing some temporal notions, though avoiding as much as possible the complexities of temporal logics. In this regard, we will basically distinguish between "persistent" normative positions, which follow the so-called law of temporal inertia or temporal persistence, and those that are temporally co-occurent with regard to some events or states of affairs. This section provides a systematic account of the basic legal concepts discussed in the paper. Rather than providing general definitions, we prefer to illustrate all notions by way of examples. We will follow the approach and notation developed in [23] . The notation adopted there is based on the use of modal operators and on formalisms taken from the Event Calculus. We prefer in this section to use this notation as it looks more intuitive, though it can be hardly embedded, as it is, within DL. These are the contexts whose logical behaviour will be caracterised in the section. With regard to actions, we distinguish two characterisations, a behavioural and productive characterisation. The first is concerned with specifying the behaviour performed by the agent, the second, the result the agent achieves. Brings Alex [the air is polluted] (Alex brings it about that the air is polluted) The productive action can also consist in making so that a conditional holds true. By applying to actions the usual deontic operators, we obtain obligations. Obligations can concern both behavioural and productive actions: Obl Does j [lecture] (it is obligatory that j lectures) 25
However, REF proposes an extension of Defeasible Logic that can represent and reason with temporalised normative positions.
Temporalised normative positions in defeasible logic
ICAIL '05
Computer Science