Related papers: A Categorial Semantic Representation of Quantum Ev…
An \'etale structure over a topological space $X$ is a continuous family of structures (in some first-order language) indexed over $X$. We give an exposition of this fundamental concept from sheaf theory and its relevance to countable model…
We outline the rationale and preliminary results of using the state context property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used and…
Quantum information brings together theories of physics and computer science. This synthesis challenges the basic intuitions of both fields. In this thesis, we show that adopting a unified and general language for process theories advances…
Semantic role theory is a widely used approach for event representation. Yet, there are multiple indications that semantic role paradigm is necessary but not sufficient to cover all elements of event structure. We conducted an analysis of…
Coherent spaces spanned by a finite number of coherent states, are introduced. Their coherence properties are studied, using the Dirac contour representation. It is shown that the corresponding projectors resolve the identity, and that they…
We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory, and of related issues such as the Kochen-Specker theorem. This extension has two main parts: the use of von Neumann…
A classical result of topos theory holds that the category of coalgebras for a Cartesian comonad on a topos is again a topos (Kock and Wraith, 1971). It is natural to refine this result to a topos-theoretic setting that includes universes.…
Quantum computation can be formulated through various models, each highlighting distinct structural and resource-theoretic aspects of quantum computational power. This paper develops a unified categorical framework that encompasses these…
Sorkin has introduced a new, observer independent, interpretation of quantum mechanics that can give a successful realist account of the 'quantum microworld' as well as explaining how classicality emerges at the level of observable events…
A scheme for an algebraic quantization of the causal sets of Sorkin et al. is presented. The suggested scenario is along the lines of a similar algebraization and quantum interpretation of finitary topological spaces due to Zapatrin and…
Quantum operations are the most widely used tool in the theory of quantum information processing, representing elementary transformations of quantum states that are composed to form complex quantum circuits. The class of quantum…
We study the central objects of symbolic dynamics, that is, subshifts and block maps, from the perspective of basic category theory, and present several natural categories with subshifts as objects and block maps as morphisms. Our main…
In the tradition of toy models of quantum mechanics in vector spaces over finite fields (e.g., Schumacher and Westmoreland's "modal quantum theory"), one finite field stands out, 2, since vectors over 2 have an interpretation as natural…
Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initiate the study of how to generalize this folklore intuition to…
While large language models (LLMs) have advanced the field of natural language processing (NLP), their "black box" nature obscures their decision-making processes. To address this, researchers developed structured approaches using higher…
Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters),…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate. Moreover, to model concurrent and…
Locales have been studied as "topologies without points", mainly by tools of category theory. While traditional topology presents a space as a set of points with specified neighborhoods, localic topology presents a space as a lattice of…
We present in this paper a reformulation of the usual set-theoretical semantics of the description logic $\mathcal{ALC}$ with general TBoxes by using categorical language. In this setting, $\mathcal{ALC}$ concepts are represented as…
A new approach is suggested to the problem of quantising causal sets, or topologies, or other such models for space-time (or space). The starting point is the observation that entities of this type can be regarded as objects in a category…