Related papers: On a new theory of models for formal mathematical …
In this research a new algebraic semantics of rough set theory including additional meta aspects is proposed. The semantics is based on enhancing the standard rough set theory with notions of 'relative ability of subsets of approximation…
One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…
In this thesis we use quasiorders on words to offer a new perspective on two well-studied problems from Formal Language Theory: deciding language inclusion and manipulating the finite automata representations of regular languages. First, we…
The present article is the first of a series whose goal is to define a logical formalism in which it is possible to reason about genetics. In this paper, we introduce the main concepts of our language whose domain of discourse consists of a…
Much theoretical work has described the ability of transformers to represent formal languages. However, linking theoretical results to empirical performance is not straightforward due to the complex interplay between the architecture, the…
We study toroidal orbifold models with topologically invariant terms in the path integral formalism and give physical interpretations of the terms from an operator formalism point of view. We briefly discuss a possibility of a new class of…
Quantitative linguistics has been allowed, in the last few decades, within the admittedly blurry boundaries of the field of complex systems. A growing host of applied mathematicians and statistical physicists devote their efforts to…
We investigate the extent to which modern, neural language models are susceptible to structural priming, the phenomenon whereby the structure of a sentence makes the same structure more probable in a follow-up sentence. We explore how…
This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to…
The modeling framework of port-Hamiltonian systems is systematically extended to constrained dynamical systems (descriptor systems, differential-algebraic equations). A new algebraically and geometrically defined system structure is…
Multiset rewriting systems provide a formalism particularly suitable for the description of biological systems. We present an extension of this formalism with additional controls on the derivations as a tool for reducing possible…
Recent advances in Language Models (LMs) have failed to mask their shortcomings particularly in the domain of reasoning. This limitation impacts several tasks, most notably those involving ontology engineering. As part of a PhD research, we…
An attractive mechanism to specify global constraints in rostering and other domains is via formal languages. For instance, the Regular and Grammar constraints specify constraints in terms of the languages accepted by an automaton and a…
To analyse and verify the safety and security properties of interactive systems, a formal specification might be necessary. There are many types of formal languages and frameworks. The decision regarding what type of formal specification…
Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…
Symbolic and logic computation systems ranging from computer algebra systems to theorem provers are finding their way into science, technology, mathematics and engineering. But such systems rely on explicitly or implicitly represented…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
Language models can produce fluent, grammatical text. Nonetheless, some maintain that language models don't really learn language and also that, even if they did, that would not be informative for the study of human learning and processing.…
The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one…
We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes several known examples. We give several examples, including a homotopy theory for…