Related papers: A Categorial Semantic Representation of Quantum Ev…
Lexical Semantics is concerned with how words encode mental representations of the world, i.e., concepts . We call this type of concepts, classification concepts . In this paper, we focus on Visual Semantics , namely on how humans build…
We introduce new foundations for relative topos theory based on stacks. One of the central results in our theory is an adjunction between the category of toposes over the topos of sheaves on a given site $({\mathcal{C}}, J)$ and that of…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
The study of classical algorithms is supported by an immense understructure, founded in logic, type, and category theory, that allows an algorithmist to reason about the sequential manipulation of data irrespective of a computation's…
The main contribution of this paper is the introduction of a dynamic logic formalism for reasoning about information flow in composite quantum systems. This builds on our previous work on a complete quantum dynamic logic for single systems.…
Reasoning about real-life events is a unifying challenge in AI and NLP that has profound utility in a variety of domains, while fallacy in high-stake applications could be catastrophic. Able to work with diverse text in these domains, large…
This paper introduces context algebras and demonstrates their application to combining logical and vector-based representations of meaning. Other approaches to this problem attempt to reproduce aspects of logical semantics within new…
Guided by grammatical structure, words compose to form sentences, and guided by discourse structure, sentences compose to form dialogues and documents. The compositional aspect of sentence and discourse units is often overlooked by machine…
Generalisation in machine learning often relies on the ability to encode structures present in data into an inductive bias of the model class. To understand the power of quantum machine learning, it is therefore crucial to identify the…
This paper is a sequel to an evolving research project on a diagrammatic methodology called thinging machine (TM). Initially, it was proposed as a base for conceptual modelling (e.g., conceptual UML) in areas such as requirement…
We provide an overview of the hybrid compositional distributional model of meaning, developed in Coecke et al. (arXiv:1003.4394v1 [cs.CL]), which is based on the categorical methods also applied to the analysis of information flow in…
There is a long history of representing a quantum state using a quasi-probability distribution: a distribution allowing negative values. In this paper we extend such representations to deal with quantum channels. The result is a convex,…
We present Temporal and Object Quantification Networks (TOQ-Nets), a new class of neuro-symbolic networks with a structural bias that enables them to learn to recognize complex relational-temporal events. This is done by including reasoning…
In this paper, we identify some categorical structures in which one can model predicative formal systems: in other words, predicative analogues of the notion of a topos, with the aim of using sheaf models to interprete predicative formal…
Applied category theory provides powerful mathematical tools for modelling processes and their composition. Symmetric monoidal categories, which involve series and parallel composition, are particularly well-suited for describing the…
Contextuality is a key signature of quantum non-classicality, which has been shown to play a central role in enabling quantum advantage for a wide range of information-processing and computational tasks. We study the logic of contextuality…
We study analysis of complex systems using a Quantitative Theory of Meaning developed as an extention of Shannon's Communication Theory. The approach consideres complexity not in terms of the manifestation of its effects which are…
The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the…
Contextuality is widely regarded as a hallmark of quantum information, yet its structural origin is often obscured by probabilistic or operational formulations. In this work, we show that non-distributive orthomodular structure need not be…
In general relativity, the causal structure between events is dynamical, but it is definite and observer-independent; events are point-like and the membership of an event A in the future or past light-cone of an event B is an…