{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KA7ISNGQWJUUAWTLIIMQ7D2MFQ","short_pith_number":"pith:KA7ISNGQ","schema_version":"1.0","canonical_sha256":"503e8934d0b269405a6b42190f8f4c2c2d51735b1bd4d9f8eb48830e649e8dfb","source":{"kind":"arxiv","id":"1502.05632","version":4},"attestation_state":"computed","paper":{"title":"Capturing k-ary Existential Second Order Logic with k-ary Inclusion-Exclusion Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Raine R\\\"onnholm","submitted_at":"2015-02-19T17:20:25Z","abstract_excerpt":"In this paper we analyze k-ary inclusion-exclusion logic, INEX[k], which is obtained by extending first order logic with k-ary inclusion and exclusion atoms. We show that every formula of INEX[k] can be expressed with a formula of k-ary existential second order logic, ESO[k]. Conversely, every formula of ESO[k] with at most k-ary free relation variables can be expressed with a formula of INEX[k]. From this it follows that, on the level of sentences, INEX[k] captures the expressive power of ESO[k].\n  We also introduce several useful operators that can be expressed in INEX[k]. In particular, we "},"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":"1502.05632","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-02-19T17:20:25Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"9fa72f4d30df4ed1250e2cc21698ab911ffe3f17737fbf7428191622e85d4ed8","abstract_canon_sha256":"34109f48ec35738ec3239d76e8674bd402508ea433caa5b7407ae1e38f9337ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:08.313668Z","signature_b64":"lBU6MbTBUoDshGVfzb5hqO2wzQ/OACSdB7irl5nDDrNJoUMmDdX+YAt+kOutLPRpNsT6pGaCq1lZbLlBpfg1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"503e8934d0b269405a6b42190f8f4c2c2d51735b1bd4d9f8eb48830e649e8dfb","last_reissued_at":"2026-05-18T00:13:08.313091Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:08.313091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Capturing k-ary Existential Second Order Logic with k-ary Inclusion-Exclusion Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Raine R\\\"onnholm","submitted_at":"2015-02-19T17:20:25Z","abstract_excerpt":"In this paper we analyze k-ary inclusion-exclusion logic, INEX[k], which is obtained by extending first order logic with k-ary inclusion and exclusion atoms. We show that every formula of INEX[k] can be expressed with a formula of k-ary existential second order logic, ESO[k]. Conversely, every formula of ESO[k] with at most k-ary free relation variables can be expressed with a formula of INEX[k]. From this it follows that, on the level of sentences, INEX[k] captures the expressive power of ESO[k].\n  We also introduce several useful operators that can be expressed in INEX[k]. In particular, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05632","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":""},"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":"1502.05632","created_at":"2026-05-18T00:13:08.313181+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.05632v4","created_at":"2026-05-18T00:13:08.313181+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05632","created_at":"2026-05-18T00:13:08.313181+00:00"},{"alias_kind":"pith_short_12","alias_value":"KA7ISNGQWJUU","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"KA7ISNGQWJUUAWTL","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"KA7ISNGQ","created_at":"2026-05-18T12:29:27.538025+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/KA7ISNGQWJUUAWTLIIMQ7D2MFQ","json":"https://pith.science/pith/KA7ISNGQWJUUAWTLIIMQ7D2MFQ.json","graph_json":"https://pith.science/api/pith-number/KA7ISNGQWJUUAWTLIIMQ7D2MFQ/graph.json","events_json":"https://pith.science/api/pith-number/KA7ISNGQWJUUAWTLIIMQ7D2MFQ/events.json","paper":"https://pith.science/paper/KA7ISNGQ"},"agent_actions":{"view_html":"https://pith.science/pith/KA7ISNGQWJUUAWTLIIMQ7D2MFQ","download_json":"https://pith.science/pith/KA7ISNGQWJUUAWTLIIMQ7D2MFQ.json","view_paper":"https://pith.science/paper/KA7ISNGQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.05632&json=true","fetch_graph":"https://pith.science/api/pith-number/KA7ISNGQWJUUAWTLIIMQ7D2MFQ/graph.json","fetch_events":"https://pith.science/api/pith-number/KA7ISNGQWJUUAWTLIIMQ7D2MFQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KA7ISNGQWJUUAWTLIIMQ7D2MFQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KA7ISNGQWJUUAWTLIIMQ7D2MFQ/action/storage_attestation","attest_author":"https://pith.science/pith/KA7ISNGQWJUUAWTLIIMQ7D2MFQ/action/author_attestation","sign_citation":"https://pith.science/pith/KA7ISNGQWJUUAWTLIIMQ7D2MFQ/action/citation_signature","submit_replication":"https://pith.science/pith/KA7ISNGQWJUUAWTLIIMQ7D2MFQ/action/replication_record"}},"created_at":"2026-05-18T00:13:08.313181+00:00","updated_at":"2026-05-18T00:13:08.313181+00:00"}