Alternative axiomatics and complexity of deliberative STIT theories

We propose two alternatives to Xu's axiomatization of the Chellas STIT. The first one also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of the Chellas STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both for the deliberative and the Chellas' STIT.Comment: Submitted to the Journal of Philosophical Logic; 13 pages excluding anne

Делегирование обязательств и авторитетные отношения агентов в логике действий

The article sets up a problem of directives and obligations that are produced by them delegation within a framework of the logic of action. We give a review of the logic of action semantics and point out their features that are substantial for the interpretation of agentive interaction in time, that set the basic conditions for delegation. We built a semantic model of authority relations between agents that are regarded as the consequences of obligations generated by those agents directives. We present an interpretation of an authority relation as an ability to provide a directive and thus formulate a candidate solution of the directives delegation problem via the description of the transitive authority relation on a set of three agents. Some comments on the properties of an authority structure that depend on the properties of agent under such an authority are given in the end.В статье, в рамках традиции логики действия, поставлена проблема делегирования указаний, порождающих обязательства агентов друг перед другом. Дан обзор существующих семантик логики действия и указаны их особенности, существенные для интерпретации взаимодействия агентов во времени, задающего общие условия делегирования. Построена семантическая модель, которая отражает связывающие агентов авторитетные отношения, рассматриваемые как следствия обязательств, порожденных отданными указаниями. Предложена интерпретация авторитетного отношения как возможности отдать указание и изложен вариант решения проблемы делегирования, данный через описание условий существования транзитивности авторитетного отношения на тройке агентов. Дан ряд замечаний относительно свойств структуры авторитетных отношений, зависящих от свойство агентов, связанных такими отношениями

Some examples formulated in a ‘seeing to it that’ logic: Illustrations, observations, problems

The paper 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.

On the computational complexity of ethics: moral tractability for minds and machines

Why should moral philosophers, moral psychologists, and machine ethicists care about computational complexity? Debates on whether artificial intelligence (AI) can or should be used to solve problems in ethical domains have mainly been driven by what AI can or cannot do in terms of human capacities. In this paper, we tackle the problem from the other end by exploring what kind of moral machines are possible based on what computational systems can or cannot do. To do so, we analyze normative ethics through the lens of computational complexity. First, we introduce computational complexity for the uninitiated reader and discuss how the complexity of ethical problems can be framed within Marr’s three levels of analysis. We then study a range of ethical problems based on consequentialism, deontology, and virtue ethics, with the aim of elucidating the complexity associated with the problems themselves (e.g., due to combinatorics, uncertainty, strategic dynamics), the computational methods employed (e.g., probability, logic, learning), and the available resources (e.g., time, knowledge, learning). The results indicate that most problems the normative frameworks pose lead to tractability issues in every category analyzed. Our investigation also provides several insights about the computational nature of normative ethics, including the differences between rule- and outcome-based moral strategies, and the implementation-variance with regard to moral resources. We then discuss the consequences complexity results have for the prospect of moral machines in virtue of the trade-off between optimality and efficiency. Finally, we elucidate how computational complexity can be used to inform both philosophical and cognitive-psychological research on human morality by advancing the moral tractability thesis