 Another foundationalist view advocates for  belief bases instead of belief states. A belief base is a set of sentences that is typically not closed under logical consequence. Its elements represent “basic” beliefs that are not derived from other beliefs. This allows us to distinguish between sentences that are explicit beliefs, like “Shakespeare wrote Hamlet” and never-thought-of deductive consequences like “Either Shakespeare wrote Hamlet or Alan Turing was born on a Monday.” Revision and contraction are then redefined to operate on belief bases, rather than belief sets. That allows for finer distinctions to be articulated, since belief bases which have the same logical closure are not treated interchangeably. For an introduction to belief bases see the relevant section of the entry on the    logic of belief revision.  For a book-length treatment, see Hansson (1999b).