Related papers: A language for mathematical knowledge management
Large language models (LLMs) offer a new empirical setting in which long-standing theories of linguistic meaning can be examined. This paper contrasts two broad approaches: social constructivist accounts associated with language games, and…
The celebrated Kleene fixed point theorem is crucial in the mathematical modelling of recursive specifications in Denotational Semantics. In this paper we discuss whether the hypothesis of the aforementioned result can be weakened. An…
In this paper we consider block languages, namely sets of words having the same length, and study the deterministic and nondeterministic state complexity of several operations on these languages. Being a subclass of finite languages, the…
Behaviors of many engineering systems are described by lumped parameter models that encapsulate the spatially distributed nature of the system into networks of lumped elements; the dynamics of such a network is governed by a system of…
Neural network techniques are widely applied to obtain high-quality distributed representations of words, i.e., word embeddings, to address text mining, information retrieval, and natural language processing tasks. Recently, efficient…
Token embeddings in multilingual BERT (m-BERT) contain both language and semantic information. We find that the representation of a language can be obtained by simply averaging the embeddings of the tokens of the language. Given this…
Natural language understanding often requires deep semantic knowledge. Expanding on previous proposals, we suggest that some important aspects of semantic knowledge can be modeled as a language model if done at an appropriate level of…
Word embeddings are substantially successful in capturing semantic relations among words. However, these lexical semantics are difficult to be interpreted. Definition modeling provides a more intuitive way to evaluate embeddings by…
Representing the semantics of linguistic items in a machine-interpretable form has been a major goal of Natural Language Processing since its earliest days. Among the range of different linguistic items, words have attracted the most…
Modern information systems are changing the idea of "data processing" to the idea of "concept processing", meaning that instead of processing words, such systems process semantic concepts which carry meaning and share contexts with other…
The purpose of this paper is to emphasize the role of language in the process of teaching and learning mathematics. We will begin with the definition of mathematics given by Cassiodorus (in its essential features repeated in Kolmogorov's…
Semantic Web is actually an extension of the current one in that it represents information more meaningfully for humans and computers alike. It enables the description of contents and services in machine-readable form, and enables…
Conceptual Engineers want to make words better. However, they often underestimate how varied our usage of words is. In this paper, we take the first steps in exploring the contextual nuances of words by creating conceptual landscapes -- 2D…
We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an…
We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such sets…
Content analysis of scientific publications is a nontrivial task, but a useful and important one for scientific information services. In the Gutenberg era it was a domain of human experts; in the digital age many machine-based methods,…
Semantics, morphology and syntax are strongly interdependent. However, the majority of computational methods for semantic change detection use distributional word representations which encode mostly semantics. We investigate an alternative…
Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…
Large-scale pre-trained language model such as BERT has achieved great success in language understanding tasks. However, it remains an open question how to utilize BERT for language generation. In this paper, we present a novel approach,…
Current definitions of notions of lexical density and semantic weight are based on the division of words into closed and open classes, and on intuition. This paper develops a computationally tractable definition of semantic weight,…