Related papers: Kleene Algebra Modulo Theories
All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always…
DatalogMTL with negation is an extension of Datalog with metric temporal operators enriched with unstratifiable negation. In this paper, we define the stable, well-founded, Kripke-Kleene, and supported model semantics for DatalogMTL with…
Knowledge Tracing (KT) serves as a fundamental component of Intelligent Tutoring Systems (ITS), enabling these systems to monitor and understand learners' progress by modeling their knowledge state. However, many existing KT models…
We consider Kleene and Stone algebras defined on the completion DM(RS) of the ordered set of rough sets induced by a reflexive relation. We focus on cases where the completion forms a spatial and completely distributive lattice. We derive…
There is an increasing interest in applying recent advances in AI to automated reasoning, as it may provide useful heuristics in reasoning over formalisms in first-order, second-order, or even meta-logics. To facilitate this research, we…
Flat iteration is a variation on the original binary version of the Kleene star operation P*Q, obtained by restricting the first argument to be a sum of atomic actions. It generalizes prefix iteration, in which the first argument is a…
Knowledge Tracing (KT) is a research field that aims to estimate a student's knowledge state through learning interactions-a crucial component of Intelligent Tutoring Systems (ITSs). Despite significant advancements, no current KT models…
Concept-based Models are a class of inherently explainable networks that improve upon standard Deep Neural Networks by providing a rationale behind their predictions using human-understandable `concepts'. With these models being highly…
Enhancing classical machine learning (ML) algorithms through quantum kernels is a rapidly growing research topic in quantum machine learning (QML). A key challenge in using kernels -- both classical and quantum -- is that ML workflows…
Mathematical reasoning is a cornerstone of artificial general intelligence and a primary benchmark for evaluating the capabilities of Large Language Models (LLMs). While state-of-the-art models show promise, they often falter when faced…
We are faced with convex quadratic programing in many contexts related to control theory, economy and robotics. In this paper, we introduce a new active set algorithm for solving such problems and analyze its possible advantages. The…
In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on…
Since the introduction by Hodges, and refinement by V\"a\"an\"anen, team semantic constructions have been used to generate expressively enriched logics still conserving nice properties, such as compactness or decidability. In contrast,…
In 1986, Kato set up a framework of conjectures relating (higher) $0$-cycles and \'etale cohomology for smooth projective schemes over finite fields or rings of integers in local fields through the homology of so-called Kato complexes. In…
Humans can develop new theorems to explore broader and more complex mathematical results. While current generative language models (LMs) have achieved significant improvement in automatically proving theorems, their ability to generate new…
The large language models (LLMs) might produce a persuasive argument within mathematical and logical fields, although such argument often includes some minor missteps, including the entire omission of side conditions, invalid inference…
Knowledge tracing (KT), a key component of an intelligent tutoring system, is a machine learning technique that estimates the mastery level of a student based on his/her past performance. The objective of KT is to predict a student's…
Typical arguments for results like Kleene's Second Recursion Theorem and the existence of self-writing computer programs bear the fingerprints of equational reasoning and combinatory logic. In fact, the connection of combinatory logic and…
We study the problem of knowledge tracing (KT) where the goal is to trace the students' knowledge mastery over time so as to make predictions on their future performance. Owing to the good representation capacity of deep neural networks…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…