Cubical Type Theoretic Navya-Ny\=aya

TL;DR

This paper formalizes Navya-Nyaya logic within cubical type theory, capturing its core structures and proving key theorems, with applications to philosophical texts and foundations.

Contribution

It provides the first CTT encoding of Navya-Nyaya concepts, establishing a stratified foundation and proving internal and meta-theoretic results.

Findings

Proved involution of abhava and other core theorems

Developed a stratified-universe foundation for Navya-Nyaya

Implemented encodings of philosophical passages and compared formalizations

Abstract

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.