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Quantum mechanics occupies a central position in contemporary science while remaining largely inaccessible to direct sensory experience. This paper proposes a roadmap to quantum aesthetics that examines how quantum concepts become aesthetic…
Complex analyses involving multiple, dependent random quantities often lead to graphical models - a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical…
We introduce SymbolicAI, a versatile and modular framework employing a logic-based approach to concept learning and flow management in generative processes. SymbolicAI enables the seamless integration of generative models with a diverse…
We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…
We present a quantum computing approach to analyzing Large Language Model (LLM) embeddings, leveraging complex-valued representations and modeling semantic relationships using quantum mechanical principles. By establishing a direct mapping…
Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel {\sigma}-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations.…
The categorical compositional distributional model of natural language provides a conceptually motivated procedure to compute the meaning of sentences, given grammatical structure and the meanings of its words. This approach has…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…
A method is given that "inverts" a logic grammar and displays it from the point of view of the logical form, rather than from that of the word string. LR-compiling techniques are used to allow a recursive-descent generation algorithm to…
Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u')…
Large Language Models (LLMs) have shown immense potential in Knowledge Graph Completion (KGC), yet bridging the modality gap between continuous graph embeddings and discrete LLM tokens remains a critical challenge. While recent…
We are in the midst of the noisy intermediate-scale quantum (NISQ) era, where quantum computers are limited by noisy gates, some of which are more error-prone than others and can render the final computation incomprehensible. Quantum…
In this work we present an intuitive construction of the quantum logical axiomatic system provided by George Mackey. The goal of this work is a detailed discussion of the results from the paper 'Physical justification for using the tensor…
At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would…
We introduce the LOv-calculus, a graphical language for reasoning about linear optical quantum circuits with so-called vacuum state auxiliary inputs. We present the axiomatics of the language and prove its soundness and completeness: two…
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such…
Substructural logics naturally support a quantitative interpretation of formulas, as they are seen as consumable resources. Distances are the quantitative counterpart of equivalence relations: they measure how much two objects are similar,…
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…
We introduce materiomusic as a generative framework linking the hierarchical structures of matter with the compositional logic of music. Across proteins, spider webs and flame dynamics, vibrational and architectural principles recur as…