Related papers: A Category Theoretic View of Contextual Types: fro…
One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce "structured cospans" as a way to study networks with inputs and outputs. Given a functor $L \colon…
Modern learning algorithms excel at producing accurate but complex models of the data. However, deploying such models in the real-world requires extra care: we must ensure their reliability, robustness, and absence of undesired biases. This…
Manual ontology construction takes time, resources, and domain specialists. Supporting a component of this process for automation or semi-automation would be good. This project and dissertation provide a Formal Concept Analysis and WordNet…
We propose a semantic foundation for logics for reasoning in settings that possess a distinction between equality of variables, a coarser equivalence of variables, and a notion of conditional independence between variables. We show that…
Our goal is to show that the standard model-theoretic concept of types can be applied in the study of order-invariant properties, i.e., properties definable in a logic in the presence of an auxiliary order relation, but not actually…
Contextualized or discourse aware commonsense inference is the task of generating coherent commonsense assertions (i.e., facts) from a given story, and a particular sentence from that story. Some problems with the task are: lack of…
A central problem in the study of resource theories is to find functions that are nonincreasing under resource conversions - termed monotones - in order to quantify resourcefulness. Various constructions of monotones appear in many…
Abstract clones serve as an algebraic presentation of the syntax of a simple type theory. From the perspective of universal algebra, they define algebraic theories like those of groups, monoids and rings. This link allows one to study the…
A variety of logical frameworks support the use of higher-order abstract syntax (HOAS) in representing formal systems. Although these systems seem superficially the same, they differ in a variety of ways; for example, how they handle a…
In a real-world corpus, knowledge frequently recurs across documents but often contains inconsistencies due to ambiguous naming, outdated information, or errors, leading to complex interrelationships between contexts. Previous research has…
We introduce a novel, logic-independent framework for the study of sequent-style proof systems, which covers a number of proof-theoretic formalisms and concrete proof systems that appear in the literature. In particular, we introduce a…
This article presents a novel approach to construct a model category structure designed to model the homotopy theory of spaces equipped with an action by the group $C_2$, where morphisms are considered to be isovariant. Our methodology…
Instance segmentation methods require large datasets with expensive and thus limited instance-level mask labels. Partially supervised instance segmentation aims to improve mask prediction with limited mask labels by utilizing the more…
Context plays an important role in visual recognition. Recent studies have shown that visual recognition networks can be fooled by placing objects in inconsistent contexts (e.g., a cow in the ocean). To model the role of contextual…
Context is essential for semantic segmentation. Due to the diverse shapes of objects and their complex layout in various scene images, the spatial scales and shapes of contexts for different objects have very large variation. It is thus…
There are several ways to formally represent families of data, such as lambda terms, in a type theory such as the dependent type theory of Coq. Mathematical representations are very compact ones and usually rely on the use of dependent…
Attributed network embedding (ANE) is to learn low-dimensional vectors so that not only the network structure but also node attributes can be preserved in the embedding space. Existing ANE models do not consider the specific combination…
Motivated by potential applications to theoretical computer science, in particular those areas where the Curry-Howard correspondence plays an important role, as well as by the ongoing search in pure mathematics for feasible approaches to…
First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type…
In view of the problem that each subchain in the chain-of-model (CoM) relies only on the information of the previous subchain and may lose long-range dependencies due to the causal mask blocking the global context flow between multi-level…