Related papers: Dynamic Tracing: a graphical language for rewritin…
A new model of symbol grounding is presented, in which the structures of natural language, logical semantics, perception and action are represented categorically, and symbol grounding is modeled via the composition of morphisms between the…
We devise a 3D scene graph representation, contact graph+ (cg+), for efficient sequential task planning. Augmented with predicate-like attributes, this contact graph-based representation abstracts scene layouts with succinct geometric…
A cycle-transversal of a graph G is a subset T of V(G) such that T intersects every cycle of G. A clique cycle-transversal, or cct for short, is a cycle-transversal which is a clique. Recognizing graphs which admit a cct can be done in…
Hypergraph categories have been rediscovered at least five times, under various names, including well-supported compact closed categories, dgs-monoidal categories, and dungeon categories. Perhaps the reason they keep being reinvented is…
It is well-known that the category of Kleisli algebras for a monoidal monad carries a canonical monoidal structure. We define the notion of a commutative graded monad and present a strictly two-categorical proof that Kleisli algebras for…
This paper gives an explicit description of the categorical operad whose algebras are precisely symmetric monoidal categories. This allows us to place the operad in a sequence of four, and therefore a sequence of four successively stricter…
Multiple-object tracking (MOT) is a challenging task that requires simultaneous reasoning about location, appearance, and identity of the objects in the scene over time. Our aim in this paper is to move beyond tracking-by-detection…
This paper presents an abstraction of Hoare logic to traced symmetric monoidal categories, a very general framework for the theory of systems. Our abstraction is based on a traced monoidal functor from an arbitrary traced monoidal category…
This is the fourth installment in a series of papers offering models of hierarchical structure for dynamical systems, using the language of polynomial functors. The operad underlying the symmetric monoidal category $(\mathbf{Poly}, \otimes,…
We present Multimodal OCR (MOCR), a document parsing paradigm that jointly parses text and graphics into unified textual representations. Unlike conventional OCR systems that focus on text recognition and leave graphical regions as cropped…
Given a braided pivotal category $\mathcal C$ and a pivotal module tensor category $\mathcal M$, we define a functor $\mathrm{Tr}_{\mathcal C}:\mathcal M \to \mathcal C$, called the associated categorified trace. By a result of…
A number of domain specific languages, such as circuits or data-science workflows, are best expressed as diagrams of boxes connected by wires. Unfortunately, functional languages have traditionally been ill-equipped to embed this sort of…
One major problem in maintaining a software system is to understand how many functional features in the system and how these features are implemented. In this paper a novel approach for locating features in code by semantic and dynamic…
A new categorical setting is defined in order to characterize the subrecursive classes belonging to complexity hierarchies. This is achieved by means of coercion functors over a symmetric monoidal category endowed with certain recursion…
A typed model of strategic term rewriting is developed. The key innovation is that generic traversal is covered. To this end, we define a typed rewriting calculus S'_{gamma}. The calculus employs a many-sorted type system extended by…
Generalized operads, also called generalized multicategories and $T$-monoids, are defined as monads within a Kleisli bicategory. With or without emphasizing their monoidal nature, generalized operads have been considered by numerous authors…
Strategy languages enable programmers to compose rewrite rules into strategies and control their application. This is useful in programming languages, e.g., for describing program transformations compositionally, but also in automated…
This is a motivating tutorial introduction to a semantic analysis of programming languages using a graphical language as the representation of terms, and graph rewriting as a representation of reduction rules. We show how the graphical…
We study rewriting for equational theories in the context of symmetric monoidal categories where there is a separable Frobenius monoid on each object. These categories, also called hypergraph categories, are increasingly relevant: Frobenius…
We introduce the normal produoidal category of monoidal contexts over an arbitrary monoidal category. In the same sense that a monoidal morphism represents a process, a monoidal context represents an incomplete process: a piece of a…