Related papers: An Introduction to Categorical Proof Theory
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
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…
This chapter provides an introduction to some basic concepts of epistemic logic, basic formal languages, their semantics, and proof systems. It also contains an overview of the handbook, and a brief history of epistemic logic and pointers…
We seize the opportunity of the publication of selected papers from the \emph{Logic, categories, semantics} workshop in the \emph{Journal of Applied Logic} to survey some current trends in logic, namely intuitionistic and linear type…
Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…
BV-categories are a recent development that aims to give categorical semantics to proofs in the logic BV. However, due to the absence of a coherence theorem on one side and a well-defined notion of proof identity for BV on the other side,…
These are the notes for a two-week mini-course given at a winter school in January 2014 as part of the thematic semester New Directions in Lie Theory at the Centre de Recherches Math\'ematiques in Montr\'eal. The goal of the course was to…
We develop semantics and syntax for bicategorical type theory. Bicategorical type theory features contexts, types, terms, and directed reductions between terms. This type theory is naturally interpreted in a class of structured…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
These notes are meant to provide a rapid introduction to triangulated categories. We start with the definition of an additive category and end with a glimps of tilting theory. Some exercises are included.
I propose a notion of theory motivated by Category theory.
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
There are many books designed to introduce category theory to either a mathematical audience or a computer science audience. In this book, our audience is the broader scientific community. We attempt to show that category theory can be…
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…
A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the…
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".…
This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the…
We examine the use of classes to formulate several categorical notions. This leads to two proposals: an explicit structure for working with subobjects, and a hierarchy of $k$-classes. We apply the latter to both ordinary and higher…
In recent years philosophers of science have explored categorical equivalence as a promising criterion for when two (physical) theories are equivalent. On the one hand, philosophers have presented several examples of theories whose…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…