  We consider a family of two-valued "fully evaluated left-sequential logics"
(FELs), of which Free FEL (defined by Staudt in 2012) is most distinguishing
(weakest) and immune to atomic side effects. Next is Memorising FEL, in which
evaluations of subexpressions are memorised. The following stronger logic is
Conditional FEL (inspired by Guzm\'an and Squier's Conditional logic, 1990).
The strongest FEL is static FEL, a sequential version of propositional logic.
We use evaluation trees as a simple, intuitive semantics and provide complete
axiomatisations for closed terms (left-sequential propositional expressions).
  For each FEL except Static FEL, we also define its three-valued version, with
a constant U for "undefinedness" and again provide complete, independent
aziomatisations, each one containing two additional axioms for U on top of the
axiomatisations of the two-valued case. In this setting, the strongest FEL is
equivalent to Bochvar's strict logic.
