相关论文: Higher-Order Coloured Unification and Natural Lang…
Deep neural networks are powerful statistical learners. However, their predictions do not come with an explanation of their process. To analyze these models, explanation methods are being developed. We present a novel explanation method,…
Hypernymy, textual entailment, and image captioning can be seen as special cases of a single visual-semantic hierarchy over words, sentences, and images. In this paper we advocate for explicitly modeling the partial order structure of this…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
The generalized coloring numbers col_r(G) (also denoted by scol_r(G)) and wcol_r(G) of a graph G were introduced by Kierstead and Yang as a generalization of the usual coloring number, and have found important theoretical and algorithmic…
The generalised colouring numbers $\mathrm{adm}_r(G)$, $\mathrm{col}_r(G)$, and $\mathrm{wcol}_r(G)$ were introduced by Kierstead and Yang as generalisations of the usual colouring number, also known as the degeneracy of a graph, and have…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
We give an introduction to the topics of our forthcoming work, in which we introduce and study new mathematical objects which we call "higher theories" of algebras, where inspiration for the term comes from William Lawvere's notion of…
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…
Color names are often made up of multiple words. As a task in natural language understanding we investigate in depth the capacity of neural networks based on sums of word embeddings (SOWE), recurrence (LSTM and GRU based RNNs) and…
Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…
We prove a Kleene theorem for higher-dimensional automata. It states that the languages they recognise are precisely the rational subsumption-closed sets of finite interval pomsets. The rational operations on these languages include a…
We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have…
The Unified Modeling Language UML is a language for specifying visualizing and documenting object oriented systems UML combines the concepts of OOA OODOMT and OOSE and is intended as a standard in the domain of object oriented analysis and…
I present the most fundamental features of an implemented system designed to manipulate representations of regular languages. The system is structured into two layers, allowing regular languages to be represented in an increasingly compact,…
Chromatic quantum contextuality is a criterion of quantum nonclassicality based on (hyper)graph coloring constraints. If a quantum hypergraph requires more colors than the number of outcomes per maximal observable (context), it lacks a…
An ordered $r$-matching is an $r$-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of $r$-dimensional orders. The theory of ordered 2-matchings is well-developed…
Language is contextual and sheaf theory provides a high level mathematical framework to model contextuality. We show how sheaf theory can model the contextual nature of natural language and how gluing can be used to provide a global…
The explanations of large language models have recently been shown to be sensitive to the randomness used for their training, creating a need to characterize this sensitivity. In this paper, we propose a characterization that questions the…