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When we think of model ensembling or ensemble modeling, there are many possibilities that come to mind in different disciplines. For example, one might think of a set of descriptions of a phenomenon in the world, perhaps a time series or a…
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
Mathematics is a highly specialized domain with its own unique set of challenges that has seen limited study in natural language processing. However, mathematics is used in a wide variety of fields and multidisciplinary research in many…
We review the philosophical framework of mathematical conceptualism as an alternative to set-theoretic foundations and show how mainstream mathematics can be developed on this basis. The paper includes an explicit axiomatization of the…
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…
I discuss the design of the method of entropic inference as a general framework for reasoning under conditions of uncertainty. The main contribution of this discussion is to emphasize the pragmatic elements in the derivation. More…
Object-oriented database systems proved very valuable at handling and administrating complex objects. In the following guidelines for embedding neural networks into such systems are presented. It is our goal to treat networks as normal data…
In systems modelling, a 'system' typically comprises located resources relative to which processes execute. One important use of logic in informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their…
We provide a setting-independent definition of reals by introducing the notion of a streak. We show that various standard constructions of reals satisfy our definition. We study the structure of reals by noting that its pieces correspond to…
The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…
We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
This paper examines the connections among various approaches to understanding concepts in philosophy, cognitive science, and machine learning, with a particular focus on their mathematical nature. By categorizing these approaches into…
This paper discusses system consequence, a central idea in the project to lift the theory of information flow to the abstract level of universal logic and the theory of institutions. The theory of information flow is a theory of distributed…
Autoformalization, the process of transforming informal mathematical propositions into verifiable formal representations, is a foundational task in automated theorem proving, offering a new perspective on the use of mathematics in both…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. In this…
In this article we focus on evolving information systems. First a delimitation of the concept of evolution is provided, resulting in a first attempt to a general theory for such evolutions. The theory makes a distinction between the…
Conceptual models as representations of real-world systems are based on diverse techniques in various disciplines but lack a framework that provides multidisciplinary ontological understanding of real-world phenomena. Concurrently, systems…
Mathematical analysis has long underpinned wireless communication theory, yet the growing complexity of next-generation systems demands increasingly sophisticated reasoning from domain experts. Recent advances in AI mathematical reasoning,…
The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing…