Doxastic Logic

Doxastic logic is a modal logic concerned with reasoning about beliefs. The term doxastic derives from the ancient Greek δόξα, doxa, which means "belief." Typically, a doxastic logic uses 'Bx' to mean "It is believed that x is the case," and the set denotes a set of beliefs. In doxastic logic, belief is treated as a modal operator.

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There is complete parallelism between a person who believes propositions and a formal system that derives propositions. Using doxastic logic, one can express the epistemic counterpart of Gödel's incompleteness theorem of metalogic, as well as Löb's theorem, and other metalogical results in terms of belief.