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- W4385876474 abstract "Abstract We 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 ( $$text {PDL}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mtext>PDL</mml:mtext> </mml:math> ), over standard translations. On the other hand, our system faithfully simulates known cyclic systems for KA and $$text {PDL}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mtext>PDL</mml:mtext> </mml:math> , 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." @default.
- W4385876474 created "2023-08-17" @default.
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- W4385876474 date "2023-08-16" @default.
- W4385876474 modified "2023-09-23" @default.
- W4385876474 title "Cyclic Hypersequent System for Transitive Closure Logic" @default.
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- W4385876474 doi "https://doi.org/10.1007/s10817-023-09675-1" @default.
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