Related papers: Modality via Iterated Enrichment
In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer…
Quantum resource theory is a cutting-edge tool used to study practical implementations of quantum mechanical principles under realistic operational constraints. It does this by modelling quantum systems as restricted classes of possible or…
This paper deals with classifying ambiguities for Multimodal Languages. It evolves the classifications and the methods of the literature on ambiguities for Natural Language and Visual Language, empirically defining an original…
We develop polytopological semantics for various constructive, intuitionistic, and G\"odel--Dummett variations of $\mathsf{K4}$ and $\mathsf{S4}$. In our models, intuitionistic and modal operators are interpreted via various topologies over…
We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of simpler components. The crucial results required by the…
In this work, we explore a double categorical framework for categories of enriched graphs, categories and the newly introduced notion of cocategories. A fundamental goal is to establish an enrichment of V-categories in V-cocategories, which…
Vision systems to see and reason about the compositional nature of visual scenes are fundamental to understanding our world. The complex relations between objects and their locations, ambiguities, and variations in the real-world…
We contribute the first denotational semantics of polymorphic dependent type theory extended by an equational theory for general (higher-order) reference types and recursive types, based on a combination of guarded recursion and…
Recently, there has been a growing interest in Multimodal Large Language Models (MLLMs) due to their remarkable potential in various tasks integrating different modalities, such as image and text, as well as applications such as image…
We introduce a new notion of recursively generated enriched term which generalizes the one studied in joint work with Rosick\'y. These new terms come together with a notion of term-interpretability, which recovers the same type of…
Semantic vectors are learned from data to express semantic relationships between elements of information, for the purpose of solving and informing downstream tasks. Other models exist that learn to map and classify supervised data. However,…
In systems modelling, a 'system' typically comprises located resources relative to which processes execute. One important use of logic in informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their…
Matching logic is a general formal framework for reasoning about a wide range of theories, with particular emphasis on programming language semantics. Notably, the intermediate language of the K semantics framework is an extension of…
We argue that locally Cartesian closed categories form a suitable doctrine for defining dependent type theories, including non-extensional ones. Using the theory of sketches, one may define syntactic categories for type theories in a style…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
In recent work, comonads and associated structures have been used to analyse a range of important notions in finite model theory, descriptive complexity and combinatorics. We extend this analysis to Hybrid logic, a widely-studied extension…
We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…
Modality is the linguistic ability to describe events with added information such as how desirable, plausible, or feasible they are. Modality is important for many NLP downstream tasks such as the detection of hedging, uncertainty,…
Time series analysis (TSA) is a longstanding research topic in the data mining community and has wide real-world significance. Compared to "richer" modalities such as language and vision, which have recently experienced explosive…
Grounding has been argued to be a crucial component towards the development of more complete and truly semantically competent artificial intelligence systems. Literature has divided into two camps: While some argue that grounding allows for…