Related papers: Tables, Memorized Semirings and Applications
Designers of autonomous agents, whether in physical or virtual environments, need to express nondeterminisim, failure, and parallelism in behaviors, as well as accounting for synchronous coordination between agents. Behavior Trees are a…
Text analytical tasks like word embedding, phrase mining, and topic modeling, are placing increasing demands as well as challenges to existing database management systems. In this paper, we provide a novel algebraic approach based on…
Two important aspects of semantic parsing for question answering are the breadth of the knowledge source and the depth of logical compositionality. While existing work trades off one aspect for another, this paper simultaneously makes…
Semilinear maps are a generalization of linear maps between vector spaces where we allow the scalar action to be twisted by a ring homomorphism such as complex conjugation. In particular, this generalization unifies the concepts of linear…
Heretofore, neural networks with external memory are restricted to single memory with lossy representations of memory interactions. A rich representation of relationships between memory pieces urges a high-order and segregated relational…
In recent years, a new class of models for multi-agent epistemic logic has emerged, based on simplicial complexes. Since then, many variants of these simplicial models have been investigated, giving rise to different logics and…
The superamalgamation property is a strong form of the amalgamation property which applies to ordered structures; it has found many applications in algebraic logic. We show that superamalgamation has some interest also from the pure…
The aim of this paper is to present a very simple set of conditions, necessary for the management of knowledge of a poset $T$ of two agents, which are partially ordered by the capabilities available in the system. We build up a formal…
Large language model (LLM) agents are increasingly deployed in structured biomedical data environments, yet they often produce fluent but overconfident outputs when reasoning over complex multi-table data. We introduce an uncertainty-aware…
Information, stored or transmitted in digital form, is often structured. Individual data records are usually represented as hierarchies of their elements. Together, records form larger structures. Information processing applications have to…
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
The large size and fast growth of data repositories, such as data lakes, has spurred the need for data discovery to help analysts find related data. The problem has become challenging as (i) a user typically does not know what datasets…
Let $\mathbf{x}_{k \times p}$ be a $k \times p$ matrix of variables and let $\mathbb{F}[\mathbf{x}_{k \times p}]$ be the polynomial ring in these variables. Given two weak compositions $\alpha,\beta \models_0 n$ of lengths $\ell(\alpha) =…
Modern order and lattice theory provides convenient mathematical tools for pattern mining, in particular for condensed irredundant representations of pattern spaces and their efficient generation. Formal Concept Analysis (FCA) offers a…
Transformative innovations in model architectures have introduced hierarchical embedding augmentation as a means to redefine the representation of tokens through multi-level semantic structures, offering enhanced adaptability to complex…
Tables are among the most powerful and practical tools for organizing and working with data. Our motivation is to equip spreadsheet programs with smart assistance capabilities. We concentrate on one particular family of tables, namely,…
Resolution-based Knowledge Representation and Reasoning (KRR) systems, such as Flora-2, Silk or Ergo, can scale to tens or hundreds of millions of facts, while supporting reasoning that includes Hilog, inheritance, defeasibility theories,…
Reasoning, the ability to logically draw conclusions from existing knowledge, is a hallmark of human. Together with perception, they constitute the two major themes of artificial intelligence. While deep learning has pushed the limit of…
In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A \otimes X \preceq B$. The purpose…
This book has seven chapters. In chapter one we give the basics needed to make this book a self contained one. Chapter two introduces the notion of interval semigroups and interval semifields and are algebraically analysed. Chapter three…