Related papers: Kleene Algebra with Observations
Algebraic $K$-theory is a homology theory that behaves very well on sufficiently nice objects such as stable $C^*$-algebras or smooth algebraic varieties, and very badly in singular situations. This survey explains how to exploit this to…
The work is devoted to Computability Logic (CoL) -- the philosophical/mathematical platform and long-term project for redeveloping classical logic after replacing truth} by computability in its underlying semantics (see…
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 show how computation of left Kan extensions can be reduced to computation of free models of cartesian (finite-limit) theories. We discuss how the standard and parallel chase compute weakly free models of regular theories and free models…
Aligning large language models (LLMs) with human preferences is inherently multi-objective: different users and evaluation criteria impose heterogeneous and often conflicting requirements on model outputs. We propose CAGE (Common-Agency…
Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for…
We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different…
A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an…
Cirquent calculus is a proof system manipulating circuit-style constructs rather than formulas. Using it, this article constructs a sound and complete axiomatization CL16 of the propositional fragment of computability logic (the…
Chart question answering (CQA) is a task used for assessing chart comprehension, which is fundamentally different from understanding natural images. CQA requires analyzing the relationships between the textual and the visual components of a…
A Cartan Calculus of Lie derivatives, differential forms, and inner derivations, based on an undeformed Cartan identity, is constructed. We attempt a classification of various types of quantum Lie algebras and present a fairly general…
We propose a cut-free cyclic system for Transitive Closure Logic (TCL) based on a form of hypersequents, suitable for automated reasoning via proof search. We show that previously proposed sequent systems are cut-free incomplete for basic…
The increasing use of machine learning in clinical decision support has been limited by the lack of transparency of many high-performing models. In clinical settings, predictions must be interpretable, auditable, and actionable. This study…
The use of Extended Logics to replace ordinary second order definability in Kleene's {\em Ramified Analytical Hierarchy} is investigated. This mirrors a similar investigation of Kennedy, Magidor and V\"a\"an\"anen \cite{KeMaVa2016} where…
We present the algebraic foundations of the HEOL setting, which combines flatness-based control and intelligent controllers, two advances in automatic control that have been proven in practice, including in industry. The result provides a…
Answering complex queries over incomplete knowledge graphs (KGs) is a challenging job. Most previous works have focused on learning entity/relation embeddings and simulating first-order logic operators with various neural networks. However,…
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…
Active learning (AL) is a learning paradigm where an active learner has to train a model (e.g., a classifier) which is in principal trained in a supervised way, but in AL it has to be done by means of a data set with initially unlabeled…
Formulae of the Lambek calculus are constructed using three binary connectives, multiplication and two divisions. We extend it using a unary connective, positive Kleene iteration. For this new operation, following its natural…
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.…