Related papers: Kleene Algebra Modulo Theories
Recurrent LLM architectures have emerged as a promising approach for improving reasoning, as they enable multi-step computation in the embedding space without generating intermediate tokens. Models such as Ouro perform reasoning by…
This paper proposes appropriate sound and complete proof systems for algebraic structures over metric spaces by combining the development of Quantitative Equational Theories (QET) with the Enriched Lawvere Theories. We extend QETs to Metric…
Knowledge Tracing (KT) aims to predict students' future performances based on their former exercises and additional information in educational settings. KT has received significant attention since it facilitates personalized experiences in…
Large language models (LLMs) have exhibited great potential in mathematical reasoning. However, there remains a performance gap in this area between existing open-source models and closed-source models such as GPT-4. In this paper, we…
Despite the rapid development of large language models (LLMs), a fundamental challenge persists: the lack of high-quality optimization modeling datasets hampers LLMs' robust modeling of practical optimization problems from natural language…
Concurrent Kleene Algebra (CKA) is a mathematical formalism to study programs that exhibit concurrent behaviour. As with previous extensions of Kleene Algebra, characterizing the free model is crucial in order to develop the foundations of…
Knowing the reasoning chains from knowledge to the predicted answers can help construct an explainable question answering (QA) system. Advances on QA explanation propose to explain the answers with entailment trees composed of multiple…
Knowledge Tracing (KT) models students' evolving knowledge states to predict future performance, serving as a foundation for personalized education. While traditional deep learning models achieve high accuracy, they often lack…
Large Language Models (LLMs) have demonstrated impressive performance in natural language processing tasks by leveraging chain of thought (CoT) that enables step-by-step thinking. Extending LLMs with multimodal capabilities is the recent…
We introduce Kleene-Varlet spaces as partially ordered sets equipped with a polarity satisfying certain additional conditions. By applying Kleene-Varlet spaces, we prove that each regular pseudocomplemented Kleene algebra is isomorphic to a…
We introduce the class of rational Kripke models and study symbolic model checking of the basic tense logic Kt and some extensions of it in models from that class. Rational Kripke models are based on (generally infinite) rational graphs,…
We introduce Concurrent NetKAT (CNetKAT), an extension of NetKAT with operators for specifying and reasoning about concurrency in scenarios where multiple packets interact through state. We provide a model of the language based on…
We introduce a new framework called linear algebraic number theory (LANT) that reformulates the number-theoretic problem as a regression model and solves it using matrix algebra. This framework restricts all computations to log space,…
Despite the impressive performance of large language models (LLMs) pretrained on vast knowledge corpora, advancing their knowledge manipulation-the ability to effectively recall, reason, and transfer relevant knowledge-remains challenging.…
We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type…
We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic…
Concurrent Kleene Algebra (CKA) is a formalism to study concurrent programs. Like previous Kleene Algebra extensions, developing a correspondence between denotational and operational perspectives is important, for both foundations and…
By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…
Recovering governing equations from data is central to scientific discovery, yet existing methods often break down under noisy, partial observations, or rely on black-box latent dynamics that obscure mechanism. We introduce MAAT (Model…
Reactive programs are ubiquitous in modern applications, and so verification is highly desirable. We present a verification strategy for reactive programs with a large or infinite state space utilising algebraic laws for reactive relations.…