Related papers: FreeCHR: An Algebraic Framework for CHR-Embeddings
We give a formal treatment of simple type theories, such as the simply-typed $\lambda$-calculus, using the framework of abstract clones. Abstract clones traditionally describe first-order structures, but by equipping them with additional…
Dealing with context dependent knowledge has led to different formalizations of the notion of context. Among them is the Contextualized Knowledge Repository (CKR) framework, which is rooted in description logics but links on the reasoning…
Program transformation is an appealing technique which allows to improve run-time efficiency, space-consumption, and more generally to optimize a given program. Essentially, it consists of a sequence of syntactic program manipulations which…
Due to the lack of structured knowledge applied in learning distributed representation of categories, existing work cannot incorporate category hierarchies into entity information.~We propose a framework that embeds entities and categories…
Category theory is the language of homological algebra, allowing us to state broadly applicable theorems and results without needing to specify the details for every instance of analogous objects. However, authors often stray from the realm…
Abstract simulation of one transition system by another is introduced as a means to simulate a potentially infinite class of similar transition sequences within a single transition sequence. This is useful for proving confluence under…
Functional data clustering is concerned with grouping functions that share similar structure, yet most existing methods implicitly operate on sampled grids, causing cluster assignments to depend on resolution, sampling density, or…
We want to establish the "braided action" (defined in the paper) of the DHR category on a universal environment algebra as a complete invariant for completely rational chiral conformal quantum field theories. The environment algebra can…
Graph transformation systems (GTS) and constraint handling rules (CHR) are non-deterministic rule-based state transition systems. CHR is well-known for its powerful confluence and program equivalence analyses, for which we provide the basis…
Abstract Meaning Representation (AMR) parsing aims to translate sentences to semantic representation with a hierarchical structure, and is recently empowered by pretrained sequence-to-sequence models. However, there exists a gap between…
Similarity-based Hierarchical Clustering (HC) is a classical unsupervised machine learning algorithm that has traditionally been solved with heuristic algorithms like Average-Linkage. Recently, Dasgupta reframed HC as a discrete…
We realize the embedding functor from pseudotensor category to tensor category in a purely algebraic setting when the pseudotensor category is the category $\mathcal{M}(H)$ of left $H$-modules, which is originally defined by Beilinson and…
Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
In this paper we show how the abstract behaviours of higher-order systems can be modelled as final coalgebras of suitable behavioural functors. These functors have the challenging peculiarity to be circularly defined with their own final…
Programming languages tend to evolve over time to use more and more concepts from theoretical computer science. Still, there is a gap between programming and pure mathematics. Not all theoretical results have realized their promising…
EHR systems lack a unified code system forrepresenting medical concepts, which acts asa barrier for the deployment of deep learningmodels in large scale to multiple clinics and hos-pitals. To overcome this problem, we…
We report on work in progress on automatic procedures for proving properties of programs written in higher-order functional languages. Our approach encodes higher-order programs directly as first-order SMT problems over Horn clauses. It is…
Many abstract interpretation frameworks and analyses for Prolog have been proposed, which seek to extract information useful for program optimization. Although motivated by practical considerations, notably making Prolog competitive with…
Solving complex, temporally-extended tasks is a long-standing problem in reinforcement learning (RL). We hypothesize that one critical element of solving such problems is the notion of compositionality. With the ability to learn concepts…
This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to…