Finite MV-effect algebras have (S1)-(S4) sequential product operations exactly when Boolean, with (S4) the fatal axiom; lower axioms are classified via nonnegative integer matrices on their Z^r representations, and exactly 34 exist on the rank-2 Boolean case.
van de Wetering, Three characterisations of the sequential product,Journal of Mathematical Physics59(2018), 082202
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The first fatal axiom for weakened sequential products on finite MV-effect algebras: Local obstruction, exact low-rank classification, and the rank-one boundary case
Finite MV-effect algebras have (S1)-(S4) sequential product operations exactly when Boolean, with (S4) the fatal axiom; lower axioms are classified via nonnegative integer matrices on their Z^r representations, and exactly 34 exist on the rank-2 Boolean case.