Cyclic Hypersequent System for Transitive Closure Logic

Abstract We propose a cut-free cyclic system for transitive closure logic (TCL) based on form of hypersequents , suitable automated reasoning via proof search. show that previously proposed sequent systems are incomplete basic validities from Kleene Algebra (KA) and propositional dynamic ( $$\text {PDL}$$ PDL ), over standard translations. On the other hand, our faithfully simulates known KA thereby inheriting their completeness results. A peculiarity is its richer correctness criterion, exhibiting ‘alternating traces’ necessitating more intricate soundness argument than traditional proofs.