Non-commutative propositional logic with short-circuit evaluation

Short-circuit evaluation denotes the semantics of propositional connectives in which second argument is evaluated only if first insufficient to determine value expression. Compound statements are from left right. widely used programming, with negation and sequential conjunction disjunction as primitives. We study question laws axiomatise short-circuit evaluation. In MSCL (memorising logic), atoms (propositional variables) evaluate true or false, a compound statement, result each atom memorised. Hence, 'Non-commutative logic evaluation' atomic evaluations cannot cause side effect. Next, we consider case that can also truth 'undefined'. For two- three-valued MSCL, present trees an intuitive provide complete independent equational axiomatisations.