Related papers: A Relational Axiomatic Framework for the Foundatio…
The evaluation mechanism of pattern matching with dynamic patterns is modelled in the Pure Pattern Calculus by one single meta-rule. This contribution presents a refinement which narrows the gap between the abstract calculus and its…
Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…
The derivation of the state of the art tensorial versions of Fundamental Measure Theory (a form of classical Density Functional Theory for hard spheres) are re-examined in the light of the recently introduced concept of global stability of…
In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressiveness of a more traditional denotation style. We will formalize a category based type and effect system to…
We present dxo, a relational system for algebra and differentiation, written in miniKanren. dxo operates over math expressions, represented as s-expressions. dxo supports addition, multiplication, exponentiation, variables (represented as…
Computational materials design often profits from the fact that some complicated contributions are not calculated for the real material, but replaced by results of models. We turn this approximation into a very general and in principle…
We propose the first framework for defining relational program logics for arbitrary monadic effects. The framework is embedded within a relational dependent type theory and is highly expressive. At the semantic level, we provide an…
Index theorem is formulated in noncommutative geometry with finite degrees of freedom by using Ginsparg-Wilson relation. It is extended to the case where the gauge symmetry is spontaneously broken. Dynamical analysis about topological…
Score-based generative models (SGMs) are generative models that are in the spotlight these days. Time-series frequently occurs in our daily life, e.g., stock data, climate data, and so on. Especially, time-series forecasting and…
In this paper, we develop a natural (empirical) relational theory for describing and modeling complex biological phenomena. We have as stepping stone the assertion: function implies structure. The theory is built upon a graph's theory…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…
Let $G$ be a locally compact second countable group equipped with an admissible non-degenerate Borel probability measure $\mu$. We generalize the notion of $\mu$-stationary systems to $\mu$-stationary $G$-factor maps $\pi: (X,\nu)\to…
We describe a graph-theoretic syntax for self-referential formulas as well as a four-valued logic to include contradictory and independent formulas. We then explore the degree to which generalized truth tables can be realized in our theory,…
What is ergonomic syntax for relations? In this first paper in a series of two, to answer the question we define regular calculi: a suitably structured functor from a category representing the syntax of regular logic to the category of…
Conceptual modeling is a strongly interdisciplinary field of research. Although numerous proposals for axiomatic foundations of the main ideas of the field exist, there is still a lack of understanding main concepts such as system, process,…
I review a number of cognate issues that, taken together, pertain to the creation of a non-reductionistic theory of multiscale coordination and present one candidate theory based on the principle of dynamical similarity.
A new seemingly weak axiomatic formulation of information algebras is given. It is shown how such information algebras can be embedded into set (information) algebras. In set algebras there is a natural relation of conditional independence…
The emergence of large-language models (LLMs) has enabled a new class of semantic data processing systems (SDPSs) to support declarative queries against unstructured documents. Existing SDPSs are, however, lacking a unified algebraic…
Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…