Related papers: Fibrational linguistics: First concepts
We define two words in a language to be connected if they express similar concepts. The network of connections among the many thousands of words that make up a language is important not only for the study of the structure and evolution of…
Figurative and metaphorical language are commonplace in discourse, and figurative expressions play an important role in communication and cognition. However, figurative language has been a relatively under-studied area in NLP, and it…
Making a linguistic theory is like making a programming language: one typically devises a type system to delineate the acceptable utterances and a denotational semantics to explain observations on their behavior. Via this connection, the…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
Modelling concept representation is a foundational problem in the study of cognition and linguistics. This work builds on the confluence of conceptual tools from G\"ardenfors semantic spaces, categorical compositional linguistics, and…
One of the ultimate goals for linguists is to find universal properties in human languages. Although words are generally considered as representing arbitrary mapping between linguistic forms and meanings, we propose a new universal law that…
We use dialgebras, generalising both algebras and coalgebras, as a complement of the standard coalgebraic framework, aimed at describing the semantics of an interactive system by the means of reaction rules. In this model, interaction is…
Logical frameworks and meta-languages form a common substrate for representing, implementing and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their design, implementation and their use in…
Experiments require human decisions in the design process, which in turn are reformulated and summarized as inputs into a system (computational or otherwise) to generate the experimental design. I leverage this system to promote a language…
G\"odel's Dialectica interpretation was conceived as a tool to obtain the consistency of Peano arithmetic via a proof of consistency of Heyting arithmetic in the 40s. In recent years, several proof-theoretic transformations, based on…
The thesis develops a view of design in a concept formation framework and outlines a language to describe both the object of the design and the process of designing. The unknown object at the outset of the design work may be seen as an…
Motivated by applications in modelling quantum systems using coalgebraic techniques, we introduce a fibred coalgebraic logic. Our approach extends the conventional predicate lifting semantics with additional modalities relating conditions…
We explain how to construct in two different ways a cartesian closed fibration of higher-order regular languages in the sense of Salvati. In the first construction, we use fibrational techniques to derive the cartesian closed fibration from…
A prototypical example of categorial grammars are those based on Lambek calculus, i.e. noncommutative intuitionistic linear logic. However, it has been noted that purely noncommutative operations are often not sufficient for modeling even…
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…
We introduce the notion of an enriched fibration, i.e. a fibration whose total category and base category are enriched in those of a monoidal fibration in an appropriate way. Furthermore, we provide a way to obtain such a structure,…
Transformer-based language models have recently achieved remarkable results in many natural language tasks. However, performance on leaderboards is generally achieved by leveraging massive amounts of training data, and rarely by encoding…
Decades of research has studied how language learning infants learn to discriminate speech sounds, segment words, and associate words with their meanings. While gradual development of such capabilities is unquestionable, the exact nature of…
Deep learning is currently the subject of intensive study. However, fundamental concepts such as representations are not formally defined -- researchers "know them when they see them" -- and there is no common language for describing and…
In this work we introduce the concepts of linguistic transformation, linguistic loop and semantic deficit. By exploiting Lie group theoretical and geometric techniques, we define invariants that capture the structural properties of a whole…