An Hypersequent Calculus for Łukasiewicz Logic Without The Merge Rule

The hypersequent system GŁ for Łukasiewicz logic presented in Ciabattoni and Metcalfe (2003) is discussed. A variant system is derived which eliminates the weakening rules and combines all of the axioms and the merge rule into a single form of axiom, resulting in a system which appears more convenient for root-first proof search