{"paper":{"title":"Declarative distributed algorithms as axiomatic theories in three-valued modal logic over semitopologies","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Distributed algorithms admit declarative axiomatizations in three-valued modal logic over semitopologies.","cross_cats":["cs.DC"],"primary_cat":"cs.LO","authors_text":"Murdoch J. Gabbay","submitted_at":"2025-12-24T12:07:25Z","abstract_excerpt":"We illustrate how to formally specify distributed algorithms as declarative axiomatic theories in a modal logic, using as illustrative examples a simple voting protocol, a simple broadcast protocol (Bracha Broadcast), and a simple agreement protocol (Crusader Agreement). The methods scale well and have been used to find errors in a proposed industrial protocol.\n  The key novelty is to use modal logic to capture a declarative, high-level representation of essential system properties -- the logical essence of the algorithm -- while abstracting away from explicit state transitions of an abstract "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We illustrate how to formally specify distributed algorithms as declarative axiomatic theories in a modal logic... using as illustrative examples a simple voting protocol, a simple broadcast protocol (Bracha Broadcast), and a simple agreement protocol (Crusader Agreement). The proofs in this paper have been formalised in Lean 4.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That three-valued modal logic over semitopologies can faithfully capture the essential correctness and resilience properties of the target distributed algorithms without omitting critical behavioral details that only appear in concrete executions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Distributed algorithms are expressed as axiomatic theories in three-valued modal logic over semitopologies, with examples including Bracha broadcast and Crusader agreement, and all proofs formalized in Lean 4.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Distributed algorithms admit declarative axiomatizations in three-valued modal logic over semitopologies.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2c1452a786757f2df7f246f6dd62852ebbf48a981dde8258d0f2d24bbd9cfc2d"},"source":{"id":"2512.21137","kind":"arxiv","version":3},"verdict":{"id":"5e90855c-1b7b-46e2-b2e0-ecb1a85026d2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T19:48:45.345253Z","strongest_claim":"We illustrate how to formally specify distributed algorithms as declarative axiomatic theories in a modal logic... using as illustrative examples a simple voting protocol, a simple broadcast protocol (Bracha Broadcast), and a simple agreement protocol (Crusader Agreement). The proofs in this paper have been formalised in Lean 4.","one_line_summary":"Distributed algorithms are expressed as axiomatic theories in three-valued modal logic over semitopologies, with examples including Bracha broadcast and Crusader agreement, and all proofs formalized in Lean 4.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That three-valued modal logic over semitopologies can faithfully capture the essential correctness and resilience properties of the target distributed algorithms without omitting critical behavioral details that only appear in concrete executions.","pith_extraction_headline":"Distributed algorithms admit declarative axiomatizations in three-valued modal logic over semitopologies."},"references":{"count":36,"sample":[{"doi":"","year":2011,"title":"Ofer Arieli, Arnon Avron, and Anna Zamansky, Ideal paraconsistent logics, Studia Logica 99 (2011), no. 1-3, 31--60","work_id":"a5bd9eb4-eaae-415d-9f26-11a6704b4a31","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Ittai Abraham, Naama Ben-David, and Sravya Yandamuri, Efficient and adaptively secure asynchronous binary agreement via binding crusader agreement, Proceedings of the 2022 ACM Symposium on Principles ","work_id":"fd7120de-2c35-411c-99e6-4aa79d99fcd5","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"184, Schloss Dagstuhl - Leibniz-Zentrum f \\\" u r Informatik, 2020, pp","work_id":"6d263d6d-7c5b-4534-bfda-2627e1202ce7","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"253, Schloss Dagstuhl - Leibniz-Zentrum f \\\" u r Informatik, 2022, pp","work_id":"adcf8f18-8e1a-4daa-ad98-b29c6a4cdac7","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Orestis Alpos, Christian Cachin, Bj \\\" o rn Tackmann, and Luca Zanolini, Asymmetric distributed trust, Distributed Computing 37 (2024), no. 3, 247--277","work_id":"714fcea5-77b6-4ab8-88b2-350c26440da7","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":36,"snapshot_sha256":"7075bf1f308fcb00cf836844a967c85b38cbf84e860446d2a9c2bef2af9ddb95","internal_anchors":0},"formal_canon":{"evidence_count":3,"snapshot_sha256":"550418395becdf57129f122ca0b48b7fe55c9c45312b93db142eb381d10cc822"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}