{"paper":{"title":"Cubical Type Theoretic Navya-Ny\\=aya","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"Cubical type theory encodes Navya-Nyaya's core structures without losing dependent delimitation or non-extensional identity.","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Mrityunjoy Panday, Sudipta Ghosh","submitted_at":"2026-05-10T05:23:46Z","abstract_excerpt":"We present a formalization of the technical language of Navya-Nyaya - the \"New Logic\" school of late-classical Indian philosophy - in CCHM De Morgan cubical type theory (CTT). Previous formalization attempts in first-order logic (Matilal), higher-order logic (Ganeri), and Martin-Lof type theory (Bhattacharyya) each lose load-bearing structure: dependent delimitation (avacchedaka), typed absence (abhava), non-extensional identity (tadatmya), or unbounded relational depth (parampara-sambandha). We argue that CTT closes this gap natively. We give CTT encodings for seven core constructs (sambandha"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We argue that CTT closes this gap natively. We give CTT encodings for seven core constructs plus the qualifier-qualificand structure and prove four signature theorems internal to the encoding.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the load-bearing structures of Navya-Nyaya (dependent delimitation, typed absence, non-extensional identity, unbounded relational depth) can be faithfully captured by the native features of CCHM De Morgan cubical type theory without introducing new postulates that alter the original meaning.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Navya-Nyaya technical language is formalized in cubical type theory with encodings for seven constructs, four internal theorems, and six metatheoretic results.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Cubical type theory encodes Navya-Nyaya's core structures without losing dependent delimitation or non-extensional identity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"112e12450b5858fff23ef47b1218c94de5a1e89d58675f39e7601a2bd9859944"},"source":{"id":"2605.12548","kind":"arxiv","version":1},"verdict":{"id":"debb4ac5-8a60-454b-8757-3866e7c042d5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T21:44:28.310326Z","strongest_claim":"We argue that CTT closes this gap natively. We give CTT encodings for seven core constructs plus the qualifier-qualificand structure and prove four signature theorems internal to the encoding.","one_line_summary":"Navya-Nyaya technical language is formalized in cubical type theory with encodings for seven constructs, four internal theorems, and six metatheoretic results.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the load-bearing structures of Navya-Nyaya (dependent delimitation, typed absence, non-extensional identity, unbounded relational depth) can be faithfully captured by the native features of CCHM De Morgan cubical type theory without introducing new postulates that alter the original meaning.","pith_extraction_headline":"Cubical type theory encodes Navya-Nyaya's core structures without losing dependent delimitation or non-extensional identity."},"references":{"count":35,"sample":[{"doi":"","year":2017,"title":"Angiuli, C., Brunerie, G., Coquand, T., Harper, R., Hou (Favonia), K.-B., Licata, D. (2017). Cartesian Cubical Type Theory. Preprint","work_id":"40962e07-b51a-4e55-9719-af83fa7550c0","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"et al.agda/cubical: A standard library for Cubical Agda.https://github","work_id":"76c263eb-9e82-4ae9-9441-d50e352fa838","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"grahawithD¯ ıpik¯ a","work_id":"45964264-6557-4361-a205-b356ab82b860","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"Awodey, S. (2018). A cubical model of homotopy type theory.Annals of Pure and Applied Logic169(12): 1270–1294","work_id":"06e68eaa-4765-4e29-a374-1e216db752c8","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1989,"title":"Bhatt, G. P. (1989).Navya-Ny¯ aya Theory of Verbal Cognition. Eastern Book Linkers","work_id":"cf618cab-8692-4633-97de-564e71d8a416","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":35,"snapshot_sha256":"6aa371713487f16ac47d480513e0ca5c86da3189ac80c123202a6afb911f4a1d","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"}