1 Modal and Meta Languages : Consistency andExpressivenessLuigia

In knowledge representation several formalisms for reasoning about knowledge in a multi agent scenario have been proposed. More speciically, we can identify a family of languages based on the use of a modal operator and another one based on the use of rst-order logic enriched with meta-level capabilities. In this paper we consider these two approaches by addressing the issues of consistency that arise from self-referentiality, their expressiveness and the methods for translating classical modal systems into meta-level rst-order formalisms. The need to reason about knowledge and reasoning arises in several applications of Arti-cial Intelligence (AI), where an explicit description of a reasoning process is used by the system (see for example Aiello et al. ACN91] and Aiello and Levi AL84]). In the past, there have been several attempts to build meta-level architectures for programming the control strategies of an inference process, thus providing a declarative speciication of domain speciic heuristics. More recently, there has been a growing interest in modeling the knowledge of an agent, which is aware of other agents and tries to take advantage of its knowledge about them. Knowledge about other agents' knowledge should thus be considered as any other source of information available to the agent for decision making about the actions to take. In particular, an agent may infer information from other agents' knowledge or ignorance of some facts; an agent may be introspective, namely capable of reasoning about its own knowledge and reasoning. Two are the main approaches to formalize an agent's knowledge and beliefs; they are here indicated as the modal and the meta approach, respectively. The modal approach has initially been developed by logicians and philosophers and later on it has attracted the interest of researchers in AI. It aims at formalizing the knowledge of an agent by a logic language augmented with a modal operator interpreted as knowledge or belief. The most common modal systems for knowledge and belief are characterized by possible-worlds semantics, which provides a descriptive view: that is to say, knowledge or belief are regarded as propositions expressing the relationship between the agent and the external world. In meta-level approaches knowledge about knowledge is represented by admitting sen