Cubical Type Theoretic Navya-Nyāya
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arXiv
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| Natura: | Preprint |
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2026
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| author | Panday, Mrityunjoy Ghosh, Sudipta |
| author_facet | Panday, Mrityunjoy Ghosh, Sudipta |
| contents | 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, avacchedaka, abhava, vyapti, tadatmya, higher relations, paryapti) plus the qualifier-qualificand structure; develop a stratified-universe foundation for the padartha system; and prove four signature theorems internal to the encoding (involution of abhava, kevalanvayi irreducibility, coextension without identity, no h-set collapse) and six metatheoretic results (soundness, conservativity, faithfulness, distinction preservation, decidability, commentarial conservativity). We close with worked encodings of fifteen Tattvacintamani passages, comparison with prior formalizations, an implementation sketch in Cubical Agda, and five distinguishing predictions - including a novel argument from Navya-Nyaya's involutive-negation doctrine for the necessity of De Morgan over Cartesian cubical foundations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12548 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cubical Type Theoretic Navya-Nyāya Panday, Mrityunjoy Ghosh, Sudipta Logic in Computer Science 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, avacchedaka, abhava, vyapti, tadatmya, higher relations, paryapti) plus the qualifier-qualificand structure; develop a stratified-universe foundation for the padartha system; and prove four signature theorems internal to the encoding (involution of abhava, kevalanvayi irreducibility, coextension without identity, no h-set collapse) and six metatheoretic results (soundness, conservativity, faithfulness, distinction preservation, decidability, commentarial conservativity). We close with worked encodings of fifteen Tattvacintamani passages, comparison with prior formalizations, an implementation sketch in Cubical Agda, and five distinguishing predictions - including a novel argument from Navya-Nyaya's involutive-negation doctrine for the necessity of De Morgan over Cartesian cubical foundations. |
| title | Cubical Type Theoretic Navya-Nyāya |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2605.12548 |