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Cyclic Proofs with Ordering Constraints

Sorin Stratulat 1, 2, 3
2 MOSEL - Proof-oriented development of computer-based systems
LORIA - FM - Department of Formal Methods
3 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
MPII - Max-Planck-Institut für Informatik, Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : CLKID ω is a sequent-based cyclic inference system able to reason on first-order logic with inductive definitions. The current approach for verifying the soundness of CLKID ω proofs is based on expensive model-checking techniques leading to an explosion in the number of states. We propose proof strategies that guarantee the soundness of a class of CLKID ω proofs if some ordering and derivability constraints are satisfied. They are inspired from previous works about cyclic well-founded induction reasoning, known to provide effective sets of ordering constraints. A derivability constraint can be checked in linear time. Under certain conditions, one can build proofs that implicitly satisfy the ordering constraints.
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Submitted on : Thursday, September 21, 2017 - 6:22:52 AM
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Sorin Stratulat. Cyclic Proofs with Ordering Constraints. TABLEAUX 2017 (26th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods), Sep 2017, Brasilia, Brazil. pp.311 - 327, ⟨10.1007/978-3-319-66902-1_19⟩. ⟨hal-01590651⟩

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