Related papers: A Universal Machine for Biform Theory Graphs
Knowledge Graph Foundation Models (KGFMs) have shown promise in enabling zero-shot reasoning over unseen graphs by learning transferable patterns. However, most existing KGFMs rely solely on graph structure, overlooking the rich semantic…
Building generalist embodied agents requires a unified system that can interpret multimodal goals, model environment dynamics, and execute reliable actions across diverse real-world tasks. Multimodal large language models (MLLMs) offer…
The Axiom-Based Atlas is a novel framework that structurally represents mathematical theorems as proof vectors over foundational axiom systems. By mapping the logical dependencies of theorems onto vectors indexed by axioms - such as those…
As the twin movements of open science and open source bring an ever greater share of the scientific process into the digital realm, new opportunities arise for the meta-scientific study of science itself, including of data science and…
Universal language representation is the holy grail in machine translation (MT). Thanks to the new neural MT approach, it seems that there are good perspectives towards this goal. In this paper, we propose a new architecture based on…
Combining ideas from distributed algorithms and alternating automata, we introduce a new class of finite graph automata that recognize precisely the languages of finite graphs definable in monadic second-order logic. By restricting…
Mathematical knowledge is a central component in science, engineering, and technology (documentation). Most of it is represented informally, and -- in contrast to published research mathematics -- subject to continual change. Unfortunately,…
An abstract machine is a theoretical model designed to perform a rigorous study of computation. Such a model usually consists of configurations, instructions, programs, inputs and outputs for the machine. In this paper we formalize these…
We propose a new approach to text semantic analysis and general corpus analysis using, as termed in this article, a "bi-gram graph" representation of a corpus. The different attributes derived from graph theory are measured and analyzed as…
This paper combines the classical model of labeled transition systems with the epistemic model for reasoning about knowledge. The result is a unifying framework for modeling and analyzing multi-agent, knowledge-based, dynamic systems. On…
It is well-known that Abstract State Machines (ASMs) can simulate "step-by-step" any type of machines (Turing machines, RAMs, etc.). We aim to overcome two facts: 1) simulation is not identification, 2) the ASMs simulating machines of some…
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
Machine translation (MT) has recently been formulated in terms of constraint-based knowledge representation and unification theories, but it is becoming more and more evident that it is not possible to design a practical MT system without…
Machine Learning (ML) systems are capable of reproducing and often amplifying undesired biases. This puts emphasis on the importance of operating under practices that enable the study and understanding of the intrinsic characteristics of ML…
Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…
Data originating from the Web, sensor readings and social media result in increasingly huge datasets. The so called Big Data comes with new scientific and technological challenges while creating new opportunities, hence the increasing…
Abstract clones serve as an algebraic presentation of the syntax of a simple type theory. From the perspective of universal algebra, they define algebraic theories like those of groups, monoids and rings. This link allows one to study the…
In this paper, we present an ontology of mathematical knowledge concepts that covers a wide range of the fields of mathematics and introduces a balanced representation between comprehensive and sensible models. We demonstrate the…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
Recently, decision trees (DT) have been used as an explainable representation of controllers (a.k.a. strategies, policies, schedulers). Although they are often very efficient and produce small and understandable controllers for discrete…