Integrating a modal logic of knowledge into terminological logics

Abstract

If we want of group of autonomous agents to act and to cooperate in a world, each of them needs knowledge about this world, about the knowledge of other agents, and about his own knowledge. To describe such knowledge we introduce the language ALC_{K} which extends the concept language ALC by a new operator Box i. Thereby, Box i,phi is to be read as "agent i knows varphi". This knowledge operator is interpreted in terms of possible worlds. That means, besides the real world, agents can imagine a number of other worlds to be possible. An agent is then said to know a fact phi if phi is true in all worlds he considers possible. In this paper we use an axiomatization of the knowledge operator which has been proposed by Moore. Thereby, knowledge of agents is interpreted such that (i) agents are able to reason on the basis of their knowledge, (ii) anything that is known by an agent is true, and (iii) if an agent knows something then he knows that he knows it. We will give tableaux-based algorithms for deciding whether a set of ALC_{K} sentences is satisfiable, and whether such a set entails a given ALC_{K} sentence.