Epistemic Extension of Propositional Preference Logics

Most of the current nonmono-tonic logics are limited to a propositional or a first-order language. This means that these formalisms cannot model an agent reasoning about the knowledge of other nonmono-tonic agents, which limits the usefulness of such formalisms in modeling communication among agents. This paper follows the approach that one can extend some of the existing nonmonotonic logics to include modal operators to denote the knowledge of other agents. We use a theory of utterance understanding as the source of our intuitions on the properties that such extended logics should exhibit. The second part of this paper discusses a methodof extending any propo-sitional preference logics into a corresponding extended logics that allows for a knowledge operator. 1 Introduction Reasoning about other agents, and in particular reasoning about the beliefs of other agents, is of fundamental importance if an intelligent system is to deal with social situations. But the logics that have been created to deal with knowledge of more than one agent (for example [Halpern and Moses, 1985]) have the limitation that the agents they model are rnonotonic. Since it is widely assumed that interesting forms of intelligence cannot be captured by mono-tonic forms of reasoning, these logics are very limited on their capacity of modeling interesting social behavior. On the other hand, most of the existing nonmonotonic logics are limited to a first-order or a propositional language. That is, although these logics capture the nonmonotonicity of the agent's reasoning, they can only model the agent when it is reasoning about "things in the world," which can be expressed in either first-order or propositional languages. In particular , the existing nonmonotonic logics cannot model an agent reasoning about the knowledge of another agent. Summarizing, the existing formal devices either model many "uninteresting" agents, or they can model only a single interesting agent. This paper addresses this problem: it describe a nonmonotonic logic that can model an agent reasoning about the knowledge of other nonmono-tonic agents. The approach taken in this paper is to extend some of the existing non-monotonic logics to include formulas that refer to another agent's knowledge. We call these logics epistemically extended. This involves extending the semantics of a nonmonotonic logics since most formalism (with the exception of default logic) are semantically limited to either propositional or first-order languages. This paper will also discuss the requirements that an epistemically extended logic should exhibit if it is …