Analytic Modal Revision for Multi-agent Systems Paolo Di Giusto 1 Guido Governatori 2 1 Regione Emilia Romagna, viale Aldo Moro 52, 40122 Bologna, Italy, e-mail coc0788@iperbole.bologna.it 2 CIT, Griffith University, Nathan, QLD 4111, Australia e-mail G.Governatori@cit.gu.edu.au Abstract. We present two models of hierarchical structured multi-agents, and we describe how to obtain a modal knowledge base from distributed sources. We then propose a computationally oriented revision procedure for modal knowledge bases. This procedure is based on a labelled tableaux calculi supplemented with a formalism to record the dependencies of the formulae. The dependencies are then used to reconstruct the minimal inconsistent sets, and the sub-formulae re- sponsible for the inconsistencies are revised according to well-defined chains of modal functions. 1 Introduction Individuals are able to build a model of the world, and so are institutions. In a common (even if a little idealized) version of this process of model building, it is assumed that a knowledge base is usually built using pieces of information collected from “outside”. The knowledge is only partial, and the process of acquiring data is unending. As data are acquired, they are also incorporated in theories: a knowledge base is not just a collection of facts, but also a system of rules connecting them. It is assumed that a set of rules is present from the beginning; new data are used for improving and refining it. It may happen that new (reliable) data are not fully compatible with the knowledge base, so we have to modify (revise) it to accommodate them. Moreover, data are acquired from several different sources, each one probing a sector of an environment (physical or conceptual). So, the process of building a knowledge base deals with distributed and partial data. As information collected from various sources may be contradictory (from one source we get p and from another source we get ¬p), using a modal language seems natural. In this way the incompatible pieces of information p and ¬p are represented as ✸p and ✸¬p, meaning that both are possible. In section 2 we present two hierarchical models of agents, then, in section 3 we show how to construct modal knowledge bases arising from the above models. In sections 4 and 5 we describe a revision procedure for modal knowledge bases, and in section 5.1 we propose a tableau formalism to be used in the process of revision. 2 Sensors, Agents, Supervisors The Basic Model (SA-model) The basic model, or SA-model, includes two compo- nents: a set of sensors and one agent. Sensors perform measurements and send the re- sults to the agent. For the sake of simplicity we assume that the sensors share the same