Related papers: A type-theoretical approach to Universal Grammar
We begin by recalling the essentially global character of universes in various models of homotopy type theory, which prevents a straightforward axiomatization of their properties using the internal language of the presheaf toposes from…
A natural next step in the evolution of constraint-based grammar formalisms from rewriting formalisms is to abstract fully away from the details of the grammar mechanism---to express syntactic theories purely in terms of the properties of…
Word segmentation is a low-level NLP task that is non-trivial for a considerable number of languages. In this paper, we present a sequence tagging framework and apply it to word segmentation for a wide range of languages with different…
The recent advances in Large Language Models (LLMs) have stimulated interest among researchers and industry professionals, particularly in their application to tasks concerning mobile user interfaces (UIs). This position paper investigates…
A repeated claim in linguistics is that the majority of linguistic utterances are unique. For example, Pinker (1994: 10), summarizing an argument by Noam Chomsky, states that "virtually every sentence that a person utters or understands is…
This work is a mathematician's attempt to understand intuitionistic logic. It can be read in two ways: as a research paper interspersed with lengthy digressions into rethinking of standard material; or as an elementary (but highly…
Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We…
Despite the well-developed cut-edge representation learning for language, most language representation models usually focus on specific level of linguistic unit, which cause great inconvenience when being confronted with handling multiple…
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…
Human syntactic structures are usually represented as graphs. Much research has focused on the mapping between such graphs and linguistic sequences, but less attention has been paid to the shapes of the graphs themselves: their topologies.…
Graphs are a generalized concept that encompasses more complex data structures than trees, such as difference lists, doubly-linked lists, skip lists, and leaf-linked trees. Normally, these structures are handled with destructive assignments…
Chomsky and others have very directly claimed that large language models (LLMs) are equally capable of learning languages that are possible and impossible for humans to learn. However, there is very little published experimental evidence to…
Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…
Language is contextual and sheaf theory provides a high level mathematical framework to model contextuality. We show how sheaf theory can model the contextual nature of natural language and how gluing can be used to provide a global…
Grammar refers to the system of rules that governs the structural organization and the semantic relations among linguistic units such as sentences, phrases, and words within a given language. In natural language processing, there remains a…
When parsing unrestricted language, wide-covering grammars often undergenerate. Undergeneration can be tackled either by sentence correction, or by grammar correction. This thesis concentrates upon automatic grammar correction (or machine…
This reports introduces a novel sound and complete semantics for first order intuitionistic logic, in the framework of category theory and by the computational interpretation of the logic based on the so-called Curry-Howard isomorphism.…
Several old and recent classes of picture grammars, that variously extend context-free string grammars in two dimensions, are based on rules that rewrite arrays of pixels. Such grammars can be unified and extended using a tiling based…
This thesis presents a computational theory of unsupervised language acquisition, precisely defining procedures for learning language from ordinary spoken or written utterances, with no explicit help from a teacher. The theory is based…
Recent breakthroughs in large language models (LLM) have stirred up global attention, and the research has been accelerating non-stop since then. Philosophers and psychologists have also been researching the structure of language for…