Related papers: Saturated Models for the Working Model Theorist
We argue for a foundational epistemic claim and a hypothesis about the production and uses of mathematical epidemiological models, exploring the consequences for our political and socio-economic lives. First, in order to make the best use…
This work is dedicated to the results were got in the model theory of the regular polygons. We give the characterization of the monoids with axiomatizable and model complete class of regular polygons. We describe the monoids with complete…
The structures $\langle M,\subseteq^M\rangle$ arising as the inclusion relation of a countable model of sufficient set theory $\langle M,\in^M\rangle$, whether well-founded or not, are all isomorphic. These structures $\langle…
We discuss several aspects of creation of adequate mathematical models in other sciences. In particular, many difficulties stem from great complexity of the source systems and the presence of a variety of uncertain factors. We illustrate…
We begin with a context more general than set theory. The basic ingredients are essentially the object and functor primitives of category theory, and the logic is weak, requiring neither the Law of Excluded Middle nor quantification. Inside…
A general framework of latent trait item response models for continuous responses is given. In contrast to classical test theory models, which traditionally distinguish between true scores and error scores, the responses are clearly linked…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
The ubiquity of machine learning based predictive models in modern society naturally leads people to ask how trustworthy those models are? In predictive modeling, it is quite common to induce a trade-off between accuracy and…
Many automated system analysis techniques (e.g., model checking, model-based testing) rely on first obtaining a model of the system under analysis. System modeling is often done manually, which is often considered as a hindrance to adopt…
Significant progress has been made in developing identification and estimation techniques for missing data problems where modeling assumptions can be described via a directed acyclic graph. The validity of results using such techniques rely…
M-estimators for Generalized Linear Models are considered under minimal assumptions. Under these preliminaries, strong convergence of the estimators are discussed and an expansion of the estimating operators are given in the non-i.i.d. case…
The rapid progress in embodied artificial intelligence has highlighted the necessity for more advanced and integrated models that can perceive, interpret, and predict environmental dynamics. In this context, World Models (WMs) have been…
I review the construction of Simplified Models for Dark Matter searches. After discussing the philosophy and some simple examples, I turn the attention to the aspect of the theoretical consistency and to the implications of the necessary…
Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for…
We present an axiomatization of Conway theories which yields,as a corollary, a very concise axiomatization of iteration theories satisfying the functorial implication for base morphisms.
Understanding the notion of a model is not always easy in logic courses. Hence, tools such as Euler diagrams are frequently applied as informal illustrations of set-theoretical models. We formally investigate Euler diagrams as an…
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,…
Prediction models are popular in medical research and practice. By predicting an outcome of interest for specific patients, these models may help inform difficult treatment decisions, and are often hailed as the poster children for…
Highly saturated models are a fundamental part of the model-theoretic machinery of nonstandard analysis. Of the two methods for producing them, ultrapowers constructed with the aid of $\kappa^+$-good ultrafilters seems by far the less…
Although models are built on the basis of some observations of reality, the concepts that derive theoretically from their definitions as well as from their characteristics and properties are not necessarily direct consequences of these…