{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:FU3YQS2WANSDJ3AASEFNLU7UWH","short_pith_number":"pith:FU3YQS2W","schema_version":"1.0","canonical_sha256":"2d37884b56036434ec00910ad5d3f4b1ee2e66e60a960d5dfbeca21a2dbfc62e","source":{"kind":"arxiv","id":"2302.01224","version":4},"attestation_state":"computed","paper":{"title":"Propositional Logics for the Lawvere Quantale","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Giorgio Bacci, Gordon Plotkin, Prakash Panangaden, Radu Mardare","submitted_at":"2023-02-02T17:04:28Z","abstract_excerpt":"Lawvere showed that generalised metric spaces are categories enriched over $[0, \\infty]$, the quantale of the positive extended reals. The statement of enrichment is a quantitative analogue of being a preorder. Towards seeking a logic for quantitative metric reasoning, we investigate three $[0,\\infty]$-valued propositional logics over the Lawvere quantale. The basic logical connectives shared by all three logics are those that can be interpreted in any quantale, viz finite conjunctions and disjunctions, tensor (addition for the Lawvere quantale) and linear implication (here a truncated subtrac"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2302.01224","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2023-02-02T17:04:28Z","cross_cats_sorted":[],"title_canon_sha256":"6e3bb32d54bb8b5d76ee10c824388adcd767e17120de7a6b606740ad208a0c40","abstract_canon_sha256":"cead4c6d7539500e9818431888d0f8ddd94a414bdcfd0efd8b69754153acb5ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:44:41.637344Z","signature_b64":"xxJBwbx6IBnrYNSXH9T2hRhjqpcMJtBW1HAkYDBVT8/Q29FB1Zpp1k48RujNBfyeFyMQOnmfzfYSCBFjDqmyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d37884b56036434ec00910ad5d3f4b1ee2e66e60a960d5dfbeca21a2dbfc62e","last_reissued_at":"2026-07-05T07:44:41.636820Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:44:41.636820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Propositional Logics for the Lawvere Quantale","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Giorgio Bacci, Gordon Plotkin, Prakash Panangaden, Radu Mardare","submitted_at":"2023-02-02T17:04:28Z","abstract_excerpt":"Lawvere showed that generalised metric spaces are categories enriched over $[0, \\infty]$, the quantale of the positive extended reals. The statement of enrichment is a quantitative analogue of being a preorder. Towards seeking a logic for quantitative metric reasoning, we investigate three $[0,\\infty]$-valued propositional logics over the Lawvere quantale. The basic logical connectives shared by all three logics are those that can be interpreted in any quantale, viz finite conjunctions and disjunctions, tensor (addition for the Lawvere quantale) and linear implication (here a truncated subtrac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.01224","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.01224/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2302.01224","created_at":"2026-07-05T07:44:41.636880+00:00"},{"alias_kind":"arxiv_version","alias_value":"2302.01224v4","created_at":"2026-07-05T07:44:41.636880+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.01224","created_at":"2026-07-05T07:44:41.636880+00:00"},{"alias_kind":"pith_short_12","alias_value":"FU3YQS2WANSD","created_at":"2026-07-05T07:44:41.636880+00:00"},{"alias_kind":"pith_short_16","alias_value":"FU3YQS2WANSDJ3AA","created_at":"2026-07-05T07:44:41.636880+00:00"},{"alias_kind":"pith_short_8","alias_value":"FU3YQS2W","created_at":"2026-07-05T07:44:41.636880+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.13348","citing_title":"Adequate Losses via Quantitative Linear Logic","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2605.13845","citing_title":"Quantitative Linear Logic for Neuro-Symbolic Learning and Verification","ref_index":13,"is_internal_anchor":false},{"citing_arxiv_id":"2605.13348","citing_title":"Adequate Losses via Quantitative Linear Logic","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2605.13845","citing_title":"Quantitative Linear Logic for Neuro-Symbolic Learning and Verification","ref_index":13,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FU3YQS2WANSDJ3AASEFNLU7UWH","json":"https://pith.science/pith/FU3YQS2WANSDJ3AASEFNLU7UWH.json","graph_json":"https://pith.science/api/pith-number/FU3YQS2WANSDJ3AASEFNLU7UWH/graph.json","events_json":"https://pith.science/api/pith-number/FU3YQS2WANSDJ3AASEFNLU7UWH/events.json","paper":"https://pith.science/paper/FU3YQS2W"},"agent_actions":{"view_html":"https://pith.science/pith/FU3YQS2WANSDJ3AASEFNLU7UWH","download_json":"https://pith.science/pith/FU3YQS2WANSDJ3AASEFNLU7UWH.json","view_paper":"https://pith.science/paper/FU3YQS2W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2302.01224&json=true","fetch_graph":"https://pith.science/api/pith-number/FU3YQS2WANSDJ3AASEFNLU7UWH/graph.json","fetch_events":"https://pith.science/api/pith-number/FU3YQS2WANSDJ3AASEFNLU7UWH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FU3YQS2WANSDJ3AASEFNLU7UWH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FU3YQS2WANSDJ3AASEFNLU7UWH/action/storage_attestation","attest_author":"https://pith.science/pith/FU3YQS2WANSDJ3AASEFNLU7UWH/action/author_attestation","sign_citation":"https://pith.science/pith/FU3YQS2WANSDJ3AASEFNLU7UWH/action/citation_signature","submit_replication":"https://pith.science/pith/FU3YQS2WANSDJ3AASEFNLU7UWH/action/replication_record"}},"created_at":"2026-07-05T07:44:41.636880+00:00","updated_at":"2026-07-05T07:44:41.636880+00:00"}