Related papers: Representing Real Numbers in a Generalized Numerat…
It has been found that Transformer-based language models have the ability to perform basic quantitative reasoning. In this paper, we propose a method for studying how these models internally represent numerical data, and use our proposal to…
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
A rational number is dyadic if it has a finite binary representation $p/2^k$, where $p$ is an integer and $k$ is a nonnegative integer. Dyadic rationals are important for numerical computations because they have an exact representation in…
The present article is devoted to the investigation of some properties of the generalized shift operator of numbers represented in terms of numeral systems with a variable alphabet.
The system PL permits the translation of abstract proofs of program correctness into programs in a variety of programming languages. A programming language satisfying certain axioms may be the target of such a translation. The system PL…
Numbers are a basic part of how humans represent and describe the world around them. As a consequence, learning effective representations of numbers is critical for the success of large language models as they become more integrated into…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
In David Schmidt's PhD work he explored the use of denotational semantics as a programming language. It was part of an effort to not only treat formal semantics as specifications but also as interpreters and input to compiler generators.…
Natural language generation systems (NLG) map non-linguistic representations into strings of words through a number of steps using intermediate representations of various levels of abstraction. Template based systems, by contrast, tend to…
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that…
Syntactic parsing is a key task in natural language processing. This task has been dominated by symbolic, grammar-based parsers. Neural networks, with their distributed representations, are challenging these methods. In this article we show…
We investigate Dirichlet-type series generated by representation functions that count the number of ways an integer can be expressed as a sum of 'k' signed higher even powers. By combining generalized theta generating functions with a…
We prove lower bounds on the length of regular expressions for finite languages by methods from arithmetic circuit complexity. First, we show a reduction: the length of a regular expression for a language $L\subseteq \{0,1\}^n$ is bounded…
Many digital functions studied in the literature, e.g., the summatory function of the base-$k$ sum-of-digits function, have a behavior showing some periodic fluctuation. Such functions are usually studied using techniques from analytic…
We examine the practicality for a user of using Answer Set Programming (ASP) for representing logical formalisms. Our example is a formalism aiming at capturing causal explanations from causal information. We show the naturalness and…
We examine the practicality for a user of using Answer Set Programming (ASP) for representing logical formalisms. We choose as an example a formalism aiming at capturing causal explanations from causal information. We provide an…
The aim of this paper is to announce the release of a novel system for abstract argumentation which is based on decomposition and dynamic programming. We provide first experimental evaluations to show the feasibility of this approach.
Humans naturally interpret numbers non-literally, effortlessly combining context, world knowledge, and speaker intent. We investigate whether large language models (LLMs) interpret numbers similarly, focusing on hyperbole and pragmatic halo…
We study word series and extended word series, classes of formal series for the analysis of some dynamical systems and their discretizations. These series are similar to but more compact than B-series. They may be composed among themselves…
The real numbers are important in both mathematics and computation theory. Computationally, real numbers can be represented in several ways; most commonly using inexact floating-point data-types, but also using exact arbitrary-precision…