@inproceedings{c90290f843f5413baf6acea6901213c5,
title = "Combinatorial Flows as Bicolored Atomic Flows",
abstract = "We introduce combinatorial flows as a graphical representation of proofs. They can be seen as a generalization of atomic flows on one side and of combinatorial proofs on the other side. From atomic flows, introduced by Guglielemi and Gundersen, they inherit the close correspondence with open deduction and the possibility of tracing the occurrences of atoms in a derivation. From combinatorial proofs, introduced by Hughes, they inherit the correctness criterion that allows to reconstruct the derivation from the flow. In fact, combinatorial flows form a proof system in the sense of Cook and Reckhow. We show how to translate between open deduction derivations and combinatorial flows, and we show how they are related to combinatorial proofs with cuts.",
keywords = "Combinatorial flows, Open deduction, Proof identity, Proof invariants",
author = "Giti Omidvar and Lutz Stra{\ss}burger",
note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 28th International Workshop on Logic, Language, Information and Computation, WoLLIC 2022 ; Conference date: 20-09-2022 Through 23-09-2022",
year = "2022",
month = jan,
day = "1",
doi = "10.1007/978-3-031-15298-6\_9",
language = "English",
isbn = "9783031152979",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "141--157",
editor = "Agata Ciabattoni and Elaine Pimentel and \{de Queiroz\}, \{Ruy J.G.B.\}",
booktitle = "Logic, Language, Information, and Computation - 28th International Workshop, WoLLIC 2022, Proceedings",
}