Related papers: Mathematical foundations of matrix syntax
An understandable concrete syntax and a comprehensible abstract syntax are two central aspects of defining a modeling language. Both representations of a language significantly overlap in their structure and also information, but may also…
As speakers turn their thoughts into sentences, they maintain a balance between the complexity of words and syntax. However, it is unclear whether this syntax-lexicon tradeoff is unique to the spoken language production that is under the…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole…
The paper presents a language model that develops syntactic structure and uses it to extract meaningful information from the word history, thus enabling the use of long distance dependencies. The model assigns probability to every joint…
Syntax-guided synthesis is a paradigm in program synthesis in which the search space of candidate solutions is constrained by a syntactic template in the form of a grammar. These syntactic constraints serve two purposes: constraining the…
This paper addresses the problem of mapping natural language sentences to lambda-calculus encodings of their meaning. We describe a learning algorithm that takes as input a training set of sentences labeled with expressions in the lambda…
The paper discusses fundamental problems in mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human…
Matrix Code gives imperative programming a mathematical semantics and heuristic power comparable in quality to functional and logic programming. A program in Matrix Code is developed incrementally from a specification in pre/post-condition…
Mathematical formulas are a fundamental and widely used component in various scientific fields, serving as a universal language for expressing complex concepts and relationships. While state-of-the-art transformer models excel in processing…
Matrix Graph Grammars (MGG) is a novel approach to the study of graph dynamics ([15]). In the present contribution we look at MGG as a formal grammar and as a model of computation, which is a necessary step in the more ambitious program of…
We provide a pipeline for generating syntax diagrams (also called railroad diagrams) from context free grammars. Syntax diagrams are a graphical representation of a context free language, which we formalize abstractly as a set of mutually…
My purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us…
When we speak, write or listen, we continuously make predictions based on our knowledge of a language's grammar. Remarkably, children acquire this grammatical knowledge within just a few years, enabling them to understand and generalise to…
It is commonly believed that knowledge of syntactic structure should improve language modeling. However, effectively and computationally efficiently incorporating syntactic structure into neural language models has been a challenging topic.…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…
We propose a new statistical model for computational linguistics. Rather than trying to estimate directly the probability distribution of a random sentence of the language, we define a Markov chain on finite sets of sentences with many…
This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely…
We propose a theoretical framework within which information on the vocabulary of a given corpus can be inferred on the basis of statistical information gathered on that corpus. Inferences can be made on the categories of the words in the…
The task of linearization is to find a grammatical order given a set of words. Traditional models use statistical methods. Syntactic linearization systems, which generate a sentence along with its syntactic tree, have shown state-of-the-art…