Related papers: Composition Conditions for Classes of Analytic Fun…
We introduce three general compositionality criteria over operational semantics and prove that, when all three are satisfied together, they guarantee weak bisimulation being a congruence. Our work is founded upon Turi and Plotkin's…
In-context learning has shown great success in i.i.d semantic parsing splits, where the training and test sets are drawn from the same distribution. In this setup, models are typically prompted with demonstrations that are similar to the…
The class of uniformly computable real functions with respect to a small subrecursive class of operators computes the elementary functions of calculus, restricted to compact subsets of their domains. The class of conditionally computable…
Service composition has become commonplace nowadays, in large part due to the increased complexity of software and supporting networks. Composition can be of many types, for instance sequential, prioritising, non-deterministic. However, a…
We propose a benchmark for evaluating compositionality in audio representations. Audio compositionality refers to representing sound scenes in terms of constituent sources and attributes, and combining them systematically. While central to…
We introduce a linearly ordered set Z and use it to prove a necessity condition for the existence of a G\^ateaux smooth norm on C(T), where T is a tree. This criterion is directly analogous to the corresponding equivalent condition for…
The Kolmogorov axioms for probability functions are placed in the context of signed meadows. A completeness theorem is stated and proven for the resulting equational theory of probability calculus. Elementary definitions of probability…
Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components - when can we…
This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…
Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.
Argument mining systems often consider contextual information, i.e. information outside of an argumentative discourse unit, when trained to accomplish tasks such as argument component identification, classification, and relation extraction.…
We find an arc-parameterization of the contour on which an given analytic function has constant modulus. This contour is seen to satisfy a differential equation which we explicitly give.
The realization theorem asserts that for a finitely presented group G, the D(2) property and the realization property are equivalent as long as G satisfies a certain finiteness condition. We show that the two properties are in fact…
We continue the study of the known equivalent reformulations of the classical moderate growth condition for weight sequences in the mixed setting; i.e. when dealing with two different sequences. This approach is becoming crucial in the…
We present work in progress on the temporal progression of compositionality in noun-noun compounds. Previous work has proposed computational methods for determining the compositionality of compounds. These methods try to automatically…
We prove that an iterated function system of similarities on $\mathbb{R}$ that satisfies the weak separation condition and has an interval as its self-similar set satisfies the stronger generalized finite type condition. It is unknown if…
A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of complete binary trees whose leaves are labeled by letters of an…
Building meaningful representations of noun compounds is not trivial since many of them scarcely appear in the corpus. To that end, composition functions approximate the distributional representation of a noun compound by combining its…
We show that the operations of composition and merging of contracts are part of the tensor product structure of the algebra of contracts.
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…