Autoepistemic

Autoepistemic logic is a branch of modal logic that deals with reasoning about one's own knowledge and beliefs. It was introduced by Robert C. Moore in 1985 as a formal system to capture the intuitive notion of "knowing that" and "believing that." The term "autoepistemic" comes from the Greek words "auto," meaning self, and "episteme," meaning knowledge.

In autoepistemic logic, an agent's beliefs are represented as a set of formulas in a modal language. The key idea is that an agent's beliefs are not arbitrary but are constrained by the agent's knowledge of what it believes and does not believe. This is captured by the notion of "stable expansions," which are sets of beliefs that are closed under certain inference rules and satisfy certain consistency conditions.

One of the main features of autoepistemic logic is its ability to handle introspective reasoning. For example, an agent can reason about its own beliefs and update them based on new information. This is done by adding or removing formulas from the set of beliefs and checking if the resulting set is still a stable expansion.

Autoepistemic logic has been applied in various areas, including artificial intelligence, where it is used to model an agent's reasoning process, and philosophy, where it is used to analyze the nature of knowledge and belief. It has also been used in the design of knowledge-based systems and in the study of non-monotonic reasoning, where the agent's beliefs can change as new information becomes available.