Cubical Type Theoretic Navya-Nyāya
For scholars of Indian logic and formal philosophy, this provides a more faithful computational representation of Navya-Nyāya constructs.
The paper formalizes Navya-Nyāya's technical language in cubical type theory, preserving structure lost in prior formalizations, and proves ten theorems plus fifteen passage encodings, with a novel argument for De Morgan cubical foundations.
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.