We define a multi-modal version of Computation Tree Logic (ctl) by extending the language with path quantifiers E δ and A δ where δ denotes one of finitely many dimensions, interpreted over Kripke structures with one total relation for each dimension. As expected, the logic is axiomatised by taking a copy of a ctl axiomatisation for each dimension. Completeness is proved by employing the completeness result for ctl to obtain a model along each dimension in turn. We also show that (...) the logic is decidable and that its satisfiability problem is no harder than the corresponding problem for ctl. We then demonstrate how Normative Systems can be conceived as a natural interpretation of such a multi-dimensional ctl logic. (shrink)

We define a multi-modal version of Computation Tree Logic (CTL) by extending the language with path quantifiers $E^\delta $ and $E^\delta $ where δ denotes one of finitely many dimensions, interpreted over Kripke structures with one total relation for each dimension. As expected, the logic is axiomatised by taking a copy of a CTL axiomatisation for each dimension. Completeness is proved by employing the completeness result for CTL to obtain a model along each dimension in turn. We also show that (...) the logic is decidable and that its satisfiability problem is no harder than the corresponding problem for CTL. We then demonstrate how Normative Systems can be conceived as a natural interpretation of such a multi-dimensional CTL logic. (shrink)

We define a multi-modal version of Computation Tree Logic (ctl) by extending the language with path quantifiers E δ and A δ where δ denotes one of finitely many dimensions, interpreted over Kripke structures with one total relation for each dimension. As expected, the logic is axiomatised by taking a copy of a ctl axiomatisation for each dimension. Completeness is proved by employing the completeness result for ctl to obtain a model along each dimension in turn. We also show that (...) the logic is decidable and that its satisfiability problem is no harder than the corresponding problem for ctl. We then demonstrate how Normative Systems can be conceived as a natural interpretation of such a multi-dimensional ctl logic. (shrink)

In this paper, we present a particular role for abductive reasoning in law by applying it in the context of an argumentation scheme for practical reasoning. We present a particular scheme, based on an established scheme for practical reasoning, that can be used to reason abductively about how an agent might have acted to reach a particular scenario, and the motivations for doing so. Plausibility here depends on a satisfactory explanation of why this particular agent followed these motivations in the (...) particular situation. The scheme is given a formal grounding in terms of action-based alternating transition systems and we illustrate the approach with a running legal example. (shrink)

There is an increasing need for norms to be embedded in technology as the widespread deployment of applications such as autonomous driving, warfare and big data analysis for crime fighting and counter-terrorism becomes ever closer. Current approaches to norms in multi-agent systems tend either to simply make prohibited actions unavailable, or to provide a set of rules which the agent is obliged to follow, either as part of its design or to avoid sanctions and punishments. In this paper we argue (...) for the position that agents should be equipped with the ability to reason about a system’s norms, by reasoning about the social and moral values that norms are designed to serve; that is, perform the sort of moral reasoning we expect of humans. In particular we highlight the need for such reasoning when circumstances are such that the rules should arguably be broken, so that the reasoning can guide agents in deciding whether to comply with the norms and, if violation is desirable, how best to violate them. One approach to enabling this is to make use of an argumentation scheme based on values and designed for practical reasoning: arguments for and against actions are generated using this scheme and agents choose between actions based on their preferences over these values. Moral reasoning then requires that agents have an acceptable set of values and an acceptable ordering on their values. We first discuss how this approach can be used to think about and justify norms in general, and then discuss how this reasoning can be used to think about when norms should be violated, and the form this violation should take. We illustrate how value based reasoning can be used to decide when and how to violate a norm using a road traffic example. We also briefly consider what makes an ordering on values acceptable, and how such an ordering might be determined. (shrink)

In this paper, we present a particular role for abductive reasoning in law by applying it in the context of an argumentation scheme for practical reasoning. We present a particular scheme, based on an established scheme for practical reasoning, that can be used to reason abductively about how an agent might have acted to reach a particular scenario, and the motivations for doing so. Plausibility here depends on a satisfactory explanation of why this particular agent followed these motivations in the (...) particular situation. The scheme is given a formal grounding in terms of action-based alternating transition systems and we illustrate the approach with a running legal example. Keywords Argumentation schemes - Abductive reasoning - Practical reasoning. (shrink)

In this paper we describe the impact that Walton’s conception of argumentation schemes had on AI and Law research. We will discuss developments in argumentation in AI and Law before Walton’s schemes became known in that community, and the issues that were current in that work. We will then show how Walton’s schemes provided a means of addressing all of those issues, and so supplied a unifying perspective from which to view argumentation in AI and Law.