{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JJCNXQXTNTUIIEEEAGLR7ZTXV2","short_pith_number":"pith:JJCNXQXT","schema_version":"1.0","canonical_sha256":"4a44dbc2f36ce884108401971fe677aeb9d2ac598cfca03aee97314e37dec33f","source":{"kind":"arxiv","id":"1608.02254","version":2},"attestation_state":"computed","paper":{"title":"Reconciling Lambek's restriction, cut-elimination, and substitution in the presence of exponential modalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CL"],"primary_cat":"math.LO","authors_text":"Andre Scedrov, Max Kanovich, Stepan Kuznetsov","submitted_at":"2016-08-07T18:17:02Z","abstract_excerpt":"The Lambek calculus can be considered as a version of non-commutative intuitionistic linear logic. One of the interesting features of the Lambek calculus is the so-called \"Lambek's restriction,\" that is, the antecedent of any provable sequent should be non-empty. In this paper we discuss ways of extending the Lambek calculus with the linear logic exponential modality while keeping Lambek's restriction. Interestingly enough, we show that for any system equipped with a reasonable exponential modality the following holds: if the system enjoys cut elimination and substitution to the full extent, t"},"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":"1608.02254","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-08-07T18:17:02Z","cross_cats_sorted":["cs.CL"],"title_canon_sha256":"9c169b8e46f9986c1bb6b81ce3b69f687953ce9a4ed99b55596e4e95da22344e","abstract_canon_sha256":"fc16948c1745363ecb19ba8ac2a734f4ab3b303a60dd6b47b12aac73b57c4222"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:42.234076Z","signature_b64":"RRd0MusqEP4Xf+uuGCBdJ6SZMC2JcmNBcj/vIFI0q+GzUJufgdXq4/BCjKr7PdJmJodkBPSMxooMyxBCP/iODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a44dbc2f36ce884108401971fe677aeb9d2ac598cfca03aee97314e37dec33f","last_reissued_at":"2026-05-17T23:46:42.233404Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:42.233404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reconciling Lambek's restriction, cut-elimination, and substitution in the presence of exponential modalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CL"],"primary_cat":"math.LO","authors_text":"Andre Scedrov, Max Kanovich, Stepan Kuznetsov","submitted_at":"2016-08-07T18:17:02Z","abstract_excerpt":"The Lambek calculus can be considered as a version of non-commutative intuitionistic linear logic. One of the interesting features of the Lambek calculus is the so-called \"Lambek's restriction,\" that is, the antecedent of any provable sequent should be non-empty. In this paper we discuss ways of extending the Lambek calculus with the linear logic exponential modality while keeping Lambek's restriction. Interestingly enough, we show that for any system equipped with a reasonable exponential modality the following holds: if the system enjoys cut elimination and substitution to the full extent, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02254","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1608.02254","created_at":"2026-05-17T23:46:42.233536+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.02254v2","created_at":"2026-05-17T23:46:42.233536+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02254","created_at":"2026-05-17T23:46:42.233536+00:00"},{"alias_kind":"pith_short_12","alias_value":"JJCNXQXTNTUI","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JJCNXQXTNTUIIEEE","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JJCNXQXT","created_at":"2026-05-18T12:30:25.849896+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JJCNXQXTNTUIIEEEAGLR7ZTXV2","json":"https://pith.science/pith/JJCNXQXTNTUIIEEEAGLR7ZTXV2.json","graph_json":"https://pith.science/api/pith-number/JJCNXQXTNTUIIEEEAGLR7ZTXV2/graph.json","events_json":"https://pith.science/api/pith-number/JJCNXQXTNTUIIEEEAGLR7ZTXV2/events.json","paper":"https://pith.science/paper/JJCNXQXT"},"agent_actions":{"view_html":"https://pith.science/pith/JJCNXQXTNTUIIEEEAGLR7ZTXV2","download_json":"https://pith.science/pith/JJCNXQXTNTUIIEEEAGLR7ZTXV2.json","view_paper":"https://pith.science/paper/JJCNXQXT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.02254&json=true","fetch_graph":"https://pith.science/api/pith-number/JJCNXQXTNTUIIEEEAGLR7ZTXV2/graph.json","fetch_events":"https://pith.science/api/pith-number/JJCNXQXTNTUIIEEEAGLR7ZTXV2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JJCNXQXTNTUIIEEEAGLR7ZTXV2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JJCNXQXTNTUIIEEEAGLR7ZTXV2/action/storage_attestation","attest_author":"https://pith.science/pith/JJCNXQXTNTUIIEEEAGLR7ZTXV2/action/author_attestation","sign_citation":"https://pith.science/pith/JJCNXQXTNTUIIEEEAGLR7ZTXV2/action/citation_signature","submit_replication":"https://pith.science/pith/JJCNXQXTNTUIIEEEAGLR7ZTXV2/action/replication_record"}},"created_at":"2026-05-17T23:46:42.233536+00:00","updated_at":"2026-05-17T23:46:42.233536+00:00"}