Related papers: Compositionality as we see it, everywhere around u…

There are many striking phenomena which are attributed to ``quantum coherence''. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical…

Compositionality -- the ability to combine familiar units like words into novel phrases and sentences -- has been the focus of intense interest in artificial intelligence in recent years. To test compositional generalization in semantic…

We accommodate the Integrated Connectionist/Symbolic Architecture (ICS) of [32] within the categorical compositional semantics (CatCo) of [13], forming a model of categorical compositional cognition (CatCog). This resolves intrinsic…

The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that…

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…

A quantum process encodes the causal structure that relates quantum operations performed in local laboratories. The process matrix formalism includes as special cases quantum mechanics on a fixed background space-time, but also allows for…

This invited paper is a passionate pitch for the significance of logic in scientific education. Logic helps focus on the essential core to identify the foundations of ideas and provides corresponding longevity with the resulting approach to…

We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…

Underlying any theory of physics is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with physical phenomena, but they also constitute our fundamental assumptions about reality. Many of the…

Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…

This paper summarises the current state-of-the art in the study of compositionality in distributional semantics, and major challenges for this area. We single out generalised quantifiers and intensional semantics as areas on which to focus…

Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated…

The possibility of a fundamental consistency between the basic quantum principles and reduction (so-called wave function reduction) is reexamined. The mathematical description of an organized macroscopic device is constructed explicitly as…

G\"odel's second incompleteness theorem is standardly understood as showing that no sufficiently strong, consistent theory of arithmetic can prove its own consistency, a result typically interpreted against a model-theoretic background in…

Complementarity is one of the main features of quantum physics that radically departs from classical notions. Here we consider the limitations that this principle imposes due to the unpredictability of measurement outcomes of incompatible…

Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…

Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…

A desired but challenging property of compiler verification is compositionality, in the sense that the compilation correctness of a program can be deduced incrementally from that of its substructures ranging from statements, functions, and…

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions…

Creativity, defined as the tendency to generate or recognize new ideas or alternatives and to make connections between seemingly unrelated phenomena, is too vast a horizon to be summed up in such a simple sentence. The extreme abstractness…