Autoepistemic logic

The autoepistemic logic is a formal logic for the representation and reasoning of knowledge about knowledge. While propositional logic can only express facts, autoepistemic logic can express knowledge and lack of knowledge about facts.

The stable model semantics, which is used to give a semantics to logic programming with negation as failure, can be seen as a simplified form of autoepistemic logic.

The syntax of autoepistemic logic extends that of propositional logic by a modal operator ${\displaystyle \Box }$ indicating knowledge: if ${\displaystyle F}$ is a formula, ${\displaystyle \Box F}$ indicates that ${\displaystyle F}$ is known. As a result, ${\displaystyle \Box \neg F}$ indicates that ${\displaystyle \neg F}$ is known and ${\displaystyle \neg \Box F}$ indicates that ${\displaystyle F}$ is not known.

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