The Knowledge, Games and Beliefs Group (KGB) is involved in a wide variety of research. The main interests of the group are the following.
When writing code, a programmer does not have to worry that the computer may suddenly decide that the next instruction is not worth its time. However, when designing a social procedure in which individual agents are performing each instruction, such a situation could arise. A successful piece of social software, i.e., procedures involving the interactions between multiple agents, will ensure that each agent can and will perform each action assigned to it, or make it rational for agents to choose actions that the designer deems socially desirable. This implies that someone designing social software should keep in mind not only the flow of information in a multi-agent setting but also game-theoretic considerations such as trying to find a mutually preferred outcome. We study many formal tools that may help a social software engineer: formal models of knowledge and beliefs, the dynamics of information in a multi-agent setting, the foundations of game theory, and logics that may be used to prove correctness of certain social procedures.
Formal Models of Knowledge and Belief
Reasoning about knowledge, in particular the knowledge of intelligent agents that reason about each other's knowledge and about the states of the world, is an interdisciplinary concern spanning computer science, mathematics and philosophy. In computer science, the formal models play a key role in areas such as distributed systems, artificial intelligence and communication. We study the formal models for reasoning about knowledge, continuing a tradition initiated in the epistemic logics devised by philosophers. Our models (using the tools provided by modal logic) illustrate the substantive philosophical and technical issues involved. Topics of current research include logical omniscience, common knowledge, group knowledge, knowledge in multi-agent systems, co-ordination and agreement and so on.
Belief Revision and Merging
Research in belief change is largely theoretical, but its motivations in the field of artificial intelligence are practical: the design of systems to maintain dynamic knowledge bases that can serve as the basis for plausible intelligent agent architectures. The standard theory for belief revision provides an elegant and powerful framework for reasoning about how a rational agent should change its beliefs when confronted with new information. However, the agents considered are extremely idealized. We have made some headway - and plan to continue to do so - on this problem by devising models that are philosophically satisfying, psychologically plausible and computationally feasible. Furthermore, intelligent agents have to be able to merge inputs received from different sources in a coherent and rational way. Information merging has much in common with the goals of social choice theory: to define operations reflecting the preferences of a society from the individual preferences of the members of the society. The problem of social choice is to find an appropriate social aggregation operation that best reflects the interests of the individuals that make up society. The problem of belief merging is to find merger operators that take multiple epistemic states as input and produce a coherent epistemic state as output. Given this connection it seems reasonable to require that any framework for the merging of information provide satisfactory ways of dealing with problems raised in social choice theory. We have investigated the link between the merging of epistemic states and important results in social choice theory.