Related papers: DEKL 2.0: Trace-Indexed Knowledge Evolution in Dep…
We describe a Martin-L\"of-style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…
We are currently designing an object oriented model which describes static and dynamical knowledge in diff{\'e}rent domains. It provides a twin conceptual level. The internal level proposes: the object structure composed of sub-objects…
Recent language models enable new opportunities for structured reasoning with text, such as the construction of intuitive, proof-like textual entailment trees without relying on brittle formal logic. However, progress in this direction has…
We present Decalf, a directed, effectful cost-aware logical framework for studying quantitative aspects of functional programs with effects. Like Calf, the language is based on an internal phase distinction between the behavior of a program…
This thesis is concerned with type-logical grammars and their practical applicability as tools of reasoning about sentence syntax and semantics. The focal point is narrowed to Dutch, a language exhibiting a large degree of word order…
Large language models (LLMs) frequently encode factual and reasoning knowledge in their internal representations that is not faithfully reflected in their surface-level outputs -- a phenomenon known as \emph{latent knowledge}. Existing…
Human knowledge is subject to uncertainties, imprecision, incompleteness and inconsistencies. Moreover, the meaning of many everyday terms is dependent on the context. That poses a huge challenge for the Semantic Web. This paper introduces…
While not obvious from its initial motivation in linear algebra, there are many context where iterated traces can be defined. In this paper we prove a very general theorem about iterated 2-categorical traces. We show that many…
Modern online education has the capacity to provide intelligent educational services by automatically analyzing substantial amounts of student behavioral data. Knowledge Tracing (KT) is one of the fundamental tasks for student behavioral…
Discrete diffusion language models (dLLMs) accelerate text generation by unmasking multiple tokens in parallel. However, parallel decoding introduces a distributional mismatch: it approximates the joint conditional using a fully factorized…
We are born with the ability to learn concepts by comparing diverse observations. This helps us to understand the new world in a compositional manner and facilitates extrapolation, as objects naturally consist of multiple concepts. In this…
Large Language Models (LLMs) serve as repositories of extensive world knowledge, enabling them to perform tasks such as question-answering and fact-checking. However, this knowledge can become obsolete as global contexts change. In this…
Bidirectional typing is a discipline in which the typing judgment is decomposed explicitly into inference and checking modes, allowing to control the flow of type information in typing rules and to specify algorithmically how they should be…
In recent years, explainable machine learning methods have been very successful. Despite their success, most explainable machine learning methods are applied to black-box models without any domain knowledge. By incorporating domain…
We study language models as evolving model organisms and ask when autoregressive next-token learning selects for world-tracking representations. For any encoding of latent world states, the Bayes-optimal next-token cross-entropy decomposes…
Learning performed over finite time is inherently irreversible. In Part~I of this series, we modeled learning as a transport process in the space of parameter distributions and derived the Epistemic Speed Limit (ESL), which lower-bounds…
As reasoning LLMs increasingly trade tokens for accuracy through deliberation, search, and self-correction, a single accuracy score can no longer tell whether those tokens buy useful reasoning, recovery from hard instances, or unnecessary…
While methods of code abstraction and reuse are widespread and well researched, methods of proof abstraction and reuse are still emerging. We consider the use of dependent types for this purpose, introducing a completely mechanical approach…
This paper proposes a categorical framework for knowledge graphs linking combinatorial graph structure with topos-theoretic semantics. Knowledge graphs are represented as labelled directed multigraphs and analysed through incidence matrices…
Pre-Requirement Specification traceability is the activity of capturing relations between requirements and their sources, in particular user needs. Requirements are formal technical specifications in the solution space; needs are natural…