Related papers: Towards a formalization of budgets
A diverse array of reasoning strategies has been proposed to elicit the capabilities of large language models. However, in this paper, we point out that traditional evaluations which focus solely on performance metrics miss a key factor:…
As deep neural models in NLP become more complex, and as a consequence opaque, the necessity to interpret them becomes greater. A burgeoning interest has emerged in rationalizing explanations to provide short and coherent justifications for…
Approaching limitations of digital computing technologies have spurred research in neuromorphic and other unconventional approaches to computing. Here we argue that if we want to systematically engineer computing systems that are based on…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
We present the basic theory of calculus on dual real numbers, and prove the counterpart of the ordinary fundamental theorem of calculus in the context of dual real numbers.
The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
We are interested in automating reasoning with and about study regulations, catering to various stakeholders, ranging from administrators, over faculty, to students at different stages. Our work builds on an extensive analysis of various…
In this work we propose a formal system for fuzzy algebraic reasoning. The sequent calculus we define is based on two kinds of propositions, capturing equality and existence of terms as members of a fuzzy set. We provide a sound semantics…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
This work proposes a complete algebraic model for classical information theory. As a precursor the essential probabilistic concepts have been defined and analyzed in the algebraic setting. Examples from probability and information theory…
The paper gives some criteria for partial sums of rational number sequences to be not rational functions and to be not algebraic functions. As an application, we study partial sums of some famous rational number sequences in mathematical…
We consider a class of linear programs on graphs with total variation regularization and a budgetary constraint. For these programs, we give a characterization of basic solutions in terms of rooted spanning forests with orientation on the…
Over the last 20 years a large number of automata-based specification theories have been proposed for modeling of discrete,real-time and probabilistic systems. We have observed a lot of shared algebraic structure between these formalisms.…
In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
In this article algebraic constructions are introduced in order to study the variety defined by a radical parametrization (a tuple of functions involving complex numbers, $n$ variables, the four field operations and radical extractions). We…
Understanding and quantifying causal relationships between variables is essential for reasoning about the physical world. In this work, we develop a resource-theoretic framework to do so. Here, we focus on the simplest nontrivial setting --…
An informal discussion of how the construction problem in algebraic geometry motivates the search for formal proof methods. Also includes a brief discussion of my own progress up to now, which concerns the formalization of category theory…