相关论文: Categorical interpretations of some key agreement …
We propose a new cubical type theory, termed (self-deprecatingly) the naive cubical type theory, and study its semantics using the universe category framework, which is similar to Uemura's categories with representable morphisms. In…
In this paper, we introduce a novel interpreting framework that learns an interpretable model based on an ontology-based sampling technique to explain agnostic prediction models. Different from existing approaches, our algorithm considers…
We introduce a complete many-valued semantics for basic normal lattice-based modal logic. This relational semantics is grounded on many-valued formal contexts from Formal Concept Analysis. We discuss an interpretation and possible…
This article reports on steps towards building a simple and accurate domain-theoretic model of generic nominally-typed OOP.
In this short note, we construct a class of models of an extension of homotopy type theory, which we call homotopy type theory with an interval type.
This entry discusses the problem of describing some communities identified in a complex network of interest, in a way allowing to interpret them. We suppose the community structure has already been detected through one of the many methods…
A theorem is derived which (i) provides a new class of subfactors which may be interpreted as generalized asymptotic subfactors, and which (ii) ensures the existence of two-dimensional local quantum field theories associated with certain…
We study quantum information and computation from a novel point of view. Our approach is based on recasting the standard axiomatic presentation of quantum mechanics, due to von Neumann, at a more abstract level, of compact closed categories…
Smart Contract Templates support legally-enforceable smart contracts, using operational parameters to connect legal agreements to standardised code. In this paper, we explore the design landscape of potential formats for storage and…
We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to…
At the heart of intuitionistic type theory lies an intuitive semantics called the "meaning explanations"; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer "proof" but "verification".…
An extension of an abstract argumentation framework, called collective argumentation, is introduced in which the attack relation is defined directly among sets of arguments. The extension turns out to be suitable, in particular, for…
The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…
Over the past two decades machine learning has permeated almost every realm of technology. At the same time, many researchers have begun using category theory as a unifying language, facilitating communication between different scientific…
In a previous paper we generalized the definition of a multilinear map to arbitrary groups and introduced two multiparty key-exchange protocols using nilpotent groups. In this paper we have a closer look at the protocols and will address…
We introduce a notion of globular multicategory with homomorphism types. These structures arise when organizing collections of "higher category-like" objects such as type theories with identity types. We show how these globular…
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
Contract-based design is a promising methodology for taming the complexity of developing sophisticated systems. A formal contract distinguishes between assumptions, which are constraints that the designer of a component puts on the…
This is a collection of introductory, expository notes on applied category theory, inspired by the 2018 Applied Category Theory Workshop, and in these notes we take a leisurely stroll through two themes (functorial semantics and…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…