arXiv subjects

Hans-Martin Will

Publications and source records attributed to Hans-Martin Will.

3 recordsLinked to original sources

arXiv2026

Typed Knowledge over Constructive Institutions

Type theories designed for mathematics or program verification need only that a proposition holds; proof irrelevance in conversion erases, at the kernel level, how a claim was established. A persistent knowledge store, by contrast, must retain that record: who established a claim, by which derivation or external tool, and under which assumptions. This volume presents the theory of Eigenius---a store of typed knowledge over constructive institutions---and develops its metatheory from that requirement. The kernel theory is a dependent type theory with cumulative universes, an impredicative universe of propositions, inductive families, and an intensional identity type. Proof irrelevance is an axiom with an explicit witness rather than a conversion rule, so proofs of a proposition are provably equal yet remain distinct terms. Definitional equality is joinability under an orthogonal rewriting system---confluent, injective on type formers, and decidable by a type-free test---while a separate subsumption judgment covers universe cumulativity, codomain-covariant function types, and declared class inclusions. We prove consistency via a set-theoretic model; develop a justification logic over the kernel's propositions to track evidence and support; organize environments as an institution so that store extensions are signature morphisms and external verdicts enter via comorphisms; formulate a typed knowledge-graph theory with records, classes, and refinements; and prove the correctness of conversion, normalization by evaluation, and bidirectional type checking relative to termination. A Lean 4 formalization accompanies the volume.

cs.LO↗

arXiv2026

Eigenius: A Typed Knowledge-Graph DBMS with Epistemic Stratification and Institution-Mediated Reasoning

As "AI Scientists" emerge to drive research via the Model Context Protocol (MCP), systems relying on ephemeral scripts will fail. The sheer scale of stateful, interconnected evidence requires a machine-walkable warranty grounded in a purpose-built database architecture. Eigenius is an open-source, typed knowledge-graph DBMS built on a single premise: answering the audit question ("what do you know, and what is your warranty?") requires a unified kernel. By tightly coupling the type system, storage engine, and integration protocol, Eigenius turns data provenance into a structural invariant rather than a property reconstructed across subsystem boundaries. The kernel rests on three pillars: a dependent type theory woven through the core, institutions acting as strongly typed integration boundaries, and a content-addressed immutable storage layer. On this foundation, epistemic status (declared/observed/derived/verified) is enforced as a strict commit-time invariant. Cross-system translations (comorphisms) are checked at commit and materialized directly into the graph as durable, first-class resources. To eliminate O(N^2) polystore bottlenecks, shared on-chain intermediate representations (IRs) collapse multi-system translations to identity. Crucially, this architecture unifies both domains of scientific epistemology: it relies on justification logic for empirical science, while embedding a fast, in-process term checker to safely evaluate formal mathematical proofs (via Lean 4) without IPC overhead. In an end-to-end recomputation of a published Nature study from fragile scripts to a materialized evidence graph, all 52 derived conclusions hold from pinned data, surfacing four machine-checked discrepancies in the original study.

cs.DB↗

arXiv2020

WaLDORf: Wasteless Language-model Distillation On Reading-comprehension

Transformer based Very Large Language Models (VLLMs) like BERT, XLNet and RoBERTa, have recently shown tremendous performance on a large variety of Natural Language Understanding (NLU) tasks. However, due to their size, these VLLMs are extremely resource intensive and cumbersome to deploy at production time. Several recent publications have looked into various ways to distil knowledge from a transformer based VLLM (most commonly BERT-Base) into a smaller model which can run much faster at inference time. Here, we propose a novel set of techniques which together produce a task-specific hybrid convolutional and transformer model, WaLDORf, that achieves state-of-the-art inference speed while still being more accurate than previous distilled models.

cs.LG↗