Related papers: Geometry of Language
Matrix syntax is a formal model of syntactic relations in language. The purpose of this paper is to explain its mathematical foundations, for an audience with some formal background. We make an axiomatic presentation, motivating each axiom…
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…
A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…
A quantitative method is suggested, where meanings of words, and grammatic rules about these, of a vocabulary are represented by real numbers. People meet randomly, and average their vocabularies if they are equal; otherwise they either…
As is the case of many signals produced by complex systems, language presents a statistical structure that is balanced between order and disorder. Here we review and extend recent results from quantitative characterisations of the degree of…
The review summarizes the main methodological concepts used in studying natural language from the perspective of complexity science and documents their applicability in identifying both universal and system-specific features of language in…
Geometry is essentially a global language, which is fully understood in different times, countries and cultures. The proof of a geometric theorem (e.g. the Pythagorean Theorem) or a geometric construction (e.g. the construction of an…
Lexical Semantics is concerned with how words encode mental representations of the world, i.e., concepts . We call this type of concepts, classification concepts . In this paper, we focus on Visual Semantics , namely on how humans build…
Human languages have evolved to be structured through repeated language learning and use. These processes introduce biases that operate during language acquisition and shape linguistic systems toward communicative efficiency. In this paper,…
Formal/symbolic semantics can provide canonical, rigid controllability and interpretability to sentence representations due to their \textit{localisation} or \textit{composition} property. How can we deliver such property to the current…
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 paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
An object--oriented approach to create a natural language understanding system is considered. The understanding program is a formal system built on the base of predicative calculus. Horn's clauses are used as well--formed formulas. An…
The ability to produce and understand an unlimited number of different sentences is a hallmark of human language. Linguists have sought to define the essence of this generative capacity using formal grammars that describe the syntactic…
We develop a system that formally represents spatial semantics concepts within natural language descriptions of spatial arrangements. The system builds on a model of spatial semantics representation according to which words in a sentence…
This paper delves into the capabilities of large language models (LLMs), specifically focusing on advancing the theoretical comprehension of chain-of-thought prompting. We investigate how LLMs can be effectively induced to generate a…
Language is highly structured, with syntactic and semantic structures, to some extent, agreed upon by speakers of the same language. With implicit or explicit awareness of such structures, humans can learn and use language efficiently and…
The orthodox interpretation of quantum theory treats the subject and the object on an equal footing. It has been suggested that the cyclical-time process, which resolves self-reference in consciousness, interconnects the observed universe…
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…
Some aspects of the physical nature of language are discussed. In particular, physical models of language must exist that are efficiently implementable. The existence requirement is essential because without physical models no communication…