4 problems

Quotient conjecture. The passage from $S$ to $\tuple{S,g}$ might correspond to taking quotients of (generalized) partial Boolean algebras.

State-extension conjecture. If state $\nu$ of $A$ satisfies PEP, then there is a state $\hat{\nu}$ of $A[\perp]$ such that

LEP--PEP converse conjecture. If PEP holds, then LEP holds:

Fixpoint conjecture. $A[\perp]^*$ coincides with iterating $A[\perp]$ to a fixpoint.