Validating Back-links of FOLID Cyclic Pre-proofs

Sorin Stratulat 1, 2
1 MOSEL - Proof-oriented development of computer-based systems
LORIA - FM - Department of Formal Methods
2 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 : Cyclic pre-proofs can be represented as sets of finite tree derivations with back-links. In the frame of the first-order logic with inductive definitions (FOLID), the nodes of the tree derivations are labelled by sequents and the back-links connect particular terminal nodes, referred to as buds, to other nodes labelled by a same sequent. However, only some back-links can constitute sound pre-proofs. Previously , it has been shown that special ordering and derivability conditions, defined along the minimal cycles of the digraph representing a particular normal form of the cyclic pre-proof, are sufficient for validating the back-links. In that approach, a same constraint could be checked several times when processing different minimal cycles, hence one may require additional recording mechanisms to avoid redundant computation in order to downgrade the time complexity to polynomial. We present a new approach that does not need to process minimal cycles. It based on a normal form that allows to define the validation conditions by taking into account only the root-bud paths from the non-singleton strongly connected components of its digraph.
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Sorin Stratulat. Validating Back-links of FOLID Cyclic Pre-proofs. CL&C'18 - Seventh International Workshop on Classical Logic and Computation, Jul 2018, Oxford, United Kingdom. Electronic Proceedings in Theoretical Computer Science, 281, pp.39--53. 〈hal-01883826〉

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