Author:
Das Anupam,Girlando Marianna
Abstract
AbstractWe propose a cut-free cyclic system for Transitive Closure Logic (TCL) based on a form of hypersequents, suitable for automated reasoning via proof search. We show that previously proposed sequent systems are cut-free incomplete for basic validities from Kleene Algebra (KA) and Propositional Dynamic Logic ($$\mathrm {PDL}$$
PDL
), over standard translations. On the other hand, our system faithfully simulates known cyclic systems for KA and $$\mathrm {PDL}$$
PDL
, thereby inheriting their completeness results. A peculiarity of our system is its richer correctness criterion, exhibiting ‘alternating traces’ and necessitating a more intricate soundness argument than for traditional cyclic proofs.
Publisher
Springer International Publishing
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