A general framework for reasoning about contradictory information and some of its applications

Abstract. This paper 2 presents a logical approach to the problem ofreasoning about information provided by several conflictin g agents.The notion of conflict which is studied here, is the notion of c ontra-diction. First, a general logical framework for reasoning with con-tradictory information is presented. This logical framework is givenby a set of axioms which describe one way of reasoning about con-tradictory information, whatever the type of information. Then, threeapplications of this framework are studied. We first examine the casewhen the information are some beliefs the agents have about the realworld. Then, we extend this work to the case when the beliefs aredated formulas described by a particular temporal logic. Finally, wepresent the case when the information provided by the agents arenorms, described by a deontic logic. 1 Introduction Collecting information provided by several agents is a very commonactivity in computer science and in every-day life also.In computer science domain, more and more, applications needto use information which is not provided by a single source of in-formation but by several. For instance, this is the case of distributeddatabases: each database stores information concerning a particularapplication domain. When considering a larger domain, one has tofederate different databases. Generally, the merging of the differentdatabasesis virtual since the databasesare locally managedin differ-ent places and by different people.This problemis called “federationof databases”,in the database community.,Federation of databases can be seen as a particular case of theproblem which consists in collecting beliefs that some agents haveabout the real world: each agent has an incomplete perception of areal situation and it is sometimes interesting to collect all these per-ceptions in order to reason about the situation, [1], [2]. The classicexample is a policeinspectorwho questionsdifferent witnesses.Eachwitness has his own beliefs concerning the crime and the inspectorhas to collect all of them in order to find the clue.For instance, one witness has said that he saw a dark blue car onthe crime place, while the second said that the car was dark greenand there were two men in it.Finally, in many organizations, computerized or not, it often hap-pen that several different regulations apply. By regulation, we meana set of sentences which express what is obligated, permitted or pro-hibited. Sometimes, these regulations are conflicting, tha t is, for in-stance, one regulation says that it is forbidden to do some action