arXiv subjects

Safal Raman Aryal

Publications and source records attributed to Safal Raman Aryal.

3 recordsLinked to original sources

arXiv2026

Studying proof data with proof theory: the case of AI-generated mathematics

I present a method for analyzing large collections of formally verified mathematical proofs (e.g. OpenAI's) grounded in some historical and philosophical musings on mathematics in the age of AI. Many of the quantities involved, such as the size of a proof term or the number of redundant steps, are already computed by work on improving automated provers, where they serve as targets. My aim is to turn them into measurements of proofs themselves: compared against a reference library and against each proof's own cut-free form, checked against theorems they must obey, and controlled for how the proofs were compiled. With these instruments, I measure how (much) machine-generated mathematics diverges from human mathematics, and find that AI-written formal proofs realize far less of the logical compression available to them than human mathematicians do (31% against 73% in mathlib, and 55% against 86% on proofs that call no automation). These figures are broadly in line with reports from those who build provers and proof-improvement tools that AI-written proofs are often longer than they need to be.

math.LO↗

arXiv2026

Coordinate-free utility theory

Standard decision theory seeks conditions under which a preference relation can be compressed into a single real-valued function. However, when preferences are incomplete or intransitive, a single function fails to capture the agent's evaluative structure. Recent literature on multi-utility representations suggests that such preferences are better represented by families of functions. This paper provides a canonical and intrinsic geometric characterization of this family. We construct the \textit{ledger group} $U(P)$, a partially ordered group that faithfully encodes the native structure of the agent's preferences in terms of trade-offs. We show that the set of all admissible utility functions is precisely the \textit{dual cone} $U^*$ of this structure. This perspective shifts the focus of utility theory from the existence of a specific map to the geometry of the measurement space itself. We demonstrate the power of this framework by explicitly reconstructing the standard multi-attribute utility representation as the intersection of the abstract dual cone with a subspace of continuous functionals, and showing the impossibility of this for a set of lexicographic preferences.

econ.TH↗

arXiv2024

Intuitionistic logic, dual intuitionistic logic, and modality

We explore various semantic understandings of dual intuitionistic logic by exploring the relationship between co-Heyting algebras and topological spaces. First, we discuss the relevant ideas in the setting of Heyting algebras and intuitionistic logic, showing organically the progression from the primordial example of lattices of open sets of topological spaces to more general ways of thinking about Heyting algebras. Then, we adapt the ideas to the dual intuitionistic setting, and use them to prove a number of interesting properties, including a deep relationship both intuitionistic and dual intuitionistic logic share through Kripke semantics to the modal logic $\mathsf{S4}$.

math.LO↗