Artificial agents will need to be aware of human moral and social norms, and able to use them in decision-making. In particular, artificial agents will need a principled approach to managing conflicting norms, which are common in human social interactions. Existing logic-based approaches suffer from normative explosion and are typically designed for deterministic environments; reward-based approaches lack principled ways of determining which normative alternatives exist in a given environment. We propose a hybrid approach, using Linear Temporal Logic (LTL) representations in Markov Decision Processes (MDPs), that manages norm conflicts in a systematic manner while accommodating domain stochasticity. We provide a proof-of-concept implementation in a simulated vacuum cleaning domain.
Social laws have proved to be a powerful and theoretically elegant framework for coordination in multi-agent systems. Most existing models of social laws assume that a designer is attempting to produce a set of constraints on agent behaviour which will ensure that some single overall desirable objective is achieved. However, this represents a gross simplification of the typical situation, where a designer may have multiple (possibly conflicting) objectives, with different priorities. Moreover, social laws, as well as bringing benefits, also have implementation costs: imposing a social law often cannot be done at zero cost. We present a model of social laws that reflects this reality: it takes into account both the fact that the designer of a social law may have multiple differently valued objectives, and that the implementation of a social law is not costneutral. In this setting, designing a social law becomes an optimisation problem, in which a designer must take into account both the benefits and costs of a social law. We investigate the issue of representing a designer's objectives, characterise the complexity of the optimal social law design problem, and consider possible constraints that lead to reductions in computational complexity. We then show how the problem of designing an optimal social law can be formulated as an integer linear program. We introduce emph Normative Temporal Logic (acro ntl ), a logic for reasoning about normative systems. acro ntl is a generalisation of the well-known branching-time temporal logic acro ctl , in which the path quantifiers @math ( on all pathsldots'') and @math ( on some pathldots'') are replaced by the indexed deontic operators @math and @math , where for example @math means @math is obligatory in the context of normative system @math ''. After defining the logic, we give a sound and complete axiomatisation, and discuss the logic's relationship to standard deontic logics. We present a symbolic representation language for models and normative systems, and identify four different model checking problems, corresponding to whether or not a model is represented symbolically or explicitly, and whether or not we are given an interpretation for the normative systems named in formulae to be checked. We show that the complexity of model checking varies from acro p -complete up to acro exptime -hard for these variations. Norms have been widely proposed as a means of coordinating and controlling the behaviour of agents in a multi-agent system. A key challenge in normative MAS is norm enforcement: how and when to restrict the agents' behaviour in order to obtain a desirable outcome? Even if a norm can be enforced theoretically, it may not be enforceable in a grounded, practical setting. In this paper we study the problem of practical norm enforcement. The key notion is that of a guard. Guards are functions which restrict the possible actions after a history of events. We propose a formal, computational model of norms, guards and norm enforcement, based on linear-time temporal logic with past operators. We show that not all norms can be enforced by such guard functions, even in the presence of unlimited computational power to reason about future events. We analyse which norms can be enforced by guards if only a fixed lookahead is available. We investigate decision problems for this question with respect to specific classes of norms, related to safety and liveness properties.