Related papers: Fundamentals of Compositional Rewriting Theory

An aggregative composition is a binary operation obeying the principle that the whole is determined by the sum of its parts. The development of graph algebras, on which the theory of formal graph languages is built, relies on aggregative…

A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…

Computability theory is traditionally conceived as the theoretical basis of informatics. Nevertheless, numerous proposals transcend computability theory, in particular by emphasizing interaction of modules, or components, parts,…

In this note we give a simple unifying proof of the undecidability of several diagrammatic properties of term rewriting systems that include: local confluence, strong confluence, diamond property, subcommutative property, and the existence…

Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms to normal forms, as well as comparing the different reduction paths that lead to those normal forms. This higher structure can be captured by…

Compositional generalization is the capability of a model to understand novel compositions composed of seen concepts. There are multiple levels of novel compositions including phrase-phrase level, phrase-word level, and word-word level.…

Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence…

Inference is a fundamental reasoning technique in probability theory. When applied to a large joint distribution, it involves updating with evidence (conditioning) in one or more components (variables) and computing the outcome in other…

We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…

A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…

Seq2seq models have been shown to struggle with compositional generalisation, i.e. generalising to new and potentially more complex structures than seen during training. Taking inspiration from grammar-based models that excel at…

We study the categorical framework for the computation of persistent homology, without reliance on a particular computational algorithm. The computation of persistent homology is commonly summarized as a matrix theorem, which we call the…

Compositional generalization is a fundamental trait in humans, allowing us to effortlessly combine known phrases to form novel sentences. Recent works have claimed that standard seq-to-seq models severely lack the ability to compositionally…

Rewriting systems are often defined as binary relations over a given set of objects. This simple definition is used to describe various properties of rewriting such as termination, confluence, normal forms etc. In this paper, we introduce a…

The goal of this paper is to formalize the notion of The Compositional Integral in The Complex Plane. We prove a convergence theorem guaranteeing its existence. We prove an analogue of Cauchy's Integral Theorem--and suggest an approach at…

We study the derivational complexity of rewrite systems whose termination is provable in the dependency pair framework using the processors for reduction pairs, dependency graphs, or the subterm criterion. We show that the derivational…

This dissertation builds a compositional cyber-physical systems theory to develop concrete semantics relating the above diverse views necessary for safety and security assurance. In this sense, composition can take two forms. The first is…

Reasoning about weak higher categorical structures constitutes a challenging task, even to the experts. One principal reason is that the language of set theory is not invariant under the weaker notions of equivalence at play, such as…

Compositional generalization is the capacity to recognize and imagine a large amount of novel combinations from known components. It is a key in human intelligence, but current neural networks generally lack such ability. This report…

For language models to generalize correctly to novel expressions, it is critical that they exploit access compositional meanings when this is justified. Even if we don't know what a "pelp" is, we can use our knowledge of numbers to…