Related papers: A Relational Axiomatic Framework for the Foundatio…
For a dust-like self-similar set (generated by IFSs with the strong separation condition), Elekes, Keleti and M\'{a}th\'{e} found an invariant, called `algebraic dependence number', by considering its generating IFSs and isometry invariant…
A thesaurus is one, out of many, possible representations of term (or word) connectivity. The terms of a thesaurus are seen as the nodes and their relationship as the links of a directed graph. The directionality of the links retains all…
We explore the idea of using a "possibilistic graphical model" as the basis for a world model that drives a dialog system. As a first step we have developed a system that uses text-based dialog to derive a model of the user's family…
Reasoning semantically in first-order logic is notoriously a challenge. This paper surveys a selection of semantically-guided or model-based methods that aim at meeting aspects of this challenge. For first-order logic we touch upon…
The conditional Gaussian nonlinear system (CGNS) is a broad class of nonlinear stochastic dynamical systems. Given the trajectories for a subset of state variables, the remaining follow a Gaussian distribution. Despite the conditionally…
Deep Generative models (DGMs) play two key roles in modern machine learning: (i) producing new information (e.g., image synthesis) and (ii) reducing dimensionality. However, traditional architectures often rely on auxiliary networks such as…
Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…
The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…
Within the gossamer numbers which extend the real numbers to include infinitesimals and infinities we prove the Fundamental Theorem of Calculus (FTC). Riemann sums are also considered in the gossamer number system, and their non-uniqueness…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
This work is the first to propose the concept of a semantic numeration system (SNS) as a certain class of context-based numeration methods. The development of the SNS concept required the introduction of fundamentally new concepts such as a…
We develop the theory of continuous and algebraic domains in constructive and predicative univalent foundations, building upon our earlier work on basic domain theory in this setting. That we work predicatively means that we do not assume…
In distributed multi-agent systems, correctness is often entangled with operational policies such as scheduling, batching, or routing, which makes systems brittle since performance-driven policy evolution may break integrity guarantees.…
The goal of this paper consists of developing a new (more physical and numerical in comparison with standard and non-standard analysis approaches) point of view on Calculus with functions assuming infinite and infinitesimal values. It uses…
We present a fully relational definition of inertial systems based in the No Arbitrariness Principle, that eliminates the need for absolute inertial frames of reference or distinguished reference systems as the "fixed stars" in order to…
We present a modification of the superposition calculus that is meant to generate consequences of sets of first-order axioms. This approach is proven to be sound and deductive-complete in the presence of redundancy elimination rules,…
Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical mechanics with applications in several fields.…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
Compositional models were introduce by Jirousek and Shenoy in the general framework of valuation-based systems. They based their theory on an axiomatic system of valuations involving not only the operations of combination and…
We reduce the principal problem of Additive Number Theory of whether an infinite sequence of integers constitutes a finite basis for the integers to a Diophantine problem involving the difference set of the sequence, by proving a formula…