Related papers: A Model Theory for the Potential Infinite
In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…
We propose terminology to classify interpretations of quantum mechanics and models that modify or complete quantum mechanics. Our focus is on models which have previously been referred to as superdeterministic (strong or weak), retrocausal…
Quantum field theory currently has a single standard mathematical characterization (the Standard Model), but no single accepted conceptual framework to interpret the mathematics. Many of these conceptualizations rely on intuitive concepts…
Subset models provide a new semantics for justifcation logic. The main idea of subset models is that evidence terms are interpreted as sets of possible worlds. A term then justifies a formula if that formula is true in each world of the…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
In a previous publication, we introduced an abstract logic via an abstract notion of quantifier. Drawing upon concepts from categorical logic, this abstract logic interprets formulas from context as subobjects in a specific category, e.g.,…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are…
In statistical analysis, many classic results require the assumption that models have finite mean or variance, including the most standard versions of the laws of large numbers and the central limit theorems. Such an assumption may not be…
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…
We present a version of arithmetic in all finite types which allows for a definition of equality at higher types for which all congruence are derivable, for which the soundness of the Dialectica interpretation is provable inside the system…
When can a model of a physical system be regarded as computable? We provide the definition of a computable physical model to answer this question. The connection between our definition and Kreisel's notion of a mechanistic theory is…
Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic…
Nominal terms extend first-order terms with binding. They lack some properties of first- and higher-order terms: Terms must be reasoned about in a context of 'freshness assumptions'; it is not always possible to 'choose a fresh variable…
The usual product $m\cdot n$ on $\mathbb{Z}$ can be viewed as the sum of $n$ terms of an arithmetic progression whose first term is $a_{1}=m-n+1$ and whose difference is $d=2$. Generalizing this idea, we define new similar product mappings,…
Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting…
A Newtonian mechanics model is essentially the model of a point body in an inertial reference frame. How to describe extended bodies in non-inertial (vibrational) reference frames with the random initial conditions? One of the most general…
A modeling formalism is proposed for the description and study of living and life-like systems. It provides an abstract conceptual model framework for real life and evolution of biological organisms. It is proposed, that this model…
There has been an increasing interest in topological semantics for epistemic logic, which has been shown to be useful for, e.g., modelling evidence, degrees of belief, and self-reference. We introduce a polytopological PDL capable of…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…