相关论文: Generic partiality for $\frac{3}{2}$-institutions

We characterize $t$-structures in stable $\infty$-categories as suitable quasicategorical factorization systems. More precisely we show that a $t$-structure $\mathfrak{t}$ on a stable $\infty$-category $\mathbf{C}$ is equivalent to a normal…

Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…

Monads can be interpreted as encoding formal expressions, or formal operations in the sense of universal algebra. We give a construction which formalizes the idea of "evaluating an expression partially": for example, "2+3" can be obtained…

When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to…

Rewriting systems are often defined as binary relations over a given set of objects. This simple definition is used to describe various properties of rewriting such as termination, confluence, normal forms etc. In this paper, we introduce a…

We propose a notion of a generalized order, which can be used for the notion of a strict partial order. We introduce a weak order to replace the usual weak order defined from a strict partial order. In a constructive setting, that usual…

For humans, visual understanding is inherently generative: given a 3D shape, we can postulate how it would look in the world; given a 2D image, we can infer the 3D structure that likely gave rise to it. We can thus translate between the 2D…

We describe an underlying right angled building structure of any graph product of buildings. We describe the automorphism group of the graph product of buildings. We show that the notion of generalized graph product of a collection of…

Ageing of publications, percentage of self-citations, and impact vary from journal to journal within fields of science. The assumption that citation and publication practices are homogenous within specialties and fields of science is…

This chapter discusses the institutional approach for organizing and maintaining ontologies. The theory of institutions was named and initially developed by Joseph Goguen and Rod Burstall. This theory, a metatheory based on category theory,…

Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the…

Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…

The aim of this work is to provide a special kind of conservative translation between abstract logics, namely an \textit{abstract Glivenko's theorem}. Firstly we define institutions on the categories of logic, algebraizable logics, and…

When we work with information from multiple sources, the formalism each employs to handle uncertainty may not be uniform. In order to be able to combine these knowledge bases of different formats, we need to first establish a common basis…

In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we…

In this paper, we introduce a method of converting implicit equations to the usual forms of functions locally without differentiability. For a system of implicit equations which are equipped with continuous functions, if there are unique…

Dualities are often supposed to be foundational, but they may come into conflict with background independence, because a hidden fixed structures is needed to define the duality transformation. This conflict can be eliminated by extending a…

Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…

Compositional generalization is the ability to generalize systematically to a new data distribution by combining known components. Although humans seem to have a great ability to generalize compositionally, state-of-the-art neural models…

A (closed) dynamical system is a notion of how things can be, together with a notion of how they may change given how they are. The idea and mathematics of closed dynamical systems has proven incredibly useful in those sciences that can…