Related papers: Quantifiers for quantum logic
We put forward a new take on the logic of quantum mechanics, following Schroedinger's point of view that it is composition which makes quantum theory what it is, rather than its particular propositional structure due to the existence of…
A semantic embedding of (constant domain) quantified conditional logic in classical higher-order logic is presented.
Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold. The algebraic notions of…
We take the view that physical quantities are values generated by processes in measurement, not pre-existent objective quantities, and that a measurement result is strictly a product of the apparatus and the subject of the measurement. We…
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…
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…
We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded…
Due to the existence of incompatible observables, the propositional calculus of a quantum system does not form a Boolean algebra but an orthomodular lattice. Such lattice can be realised as a lattice of subspaces on a real, complex or…
It is well known that classical and quantum theories carry distinct types of representations, each type of representation corresponding to possible values of generalized charges in the classical or quantum context. This paper demonstrates a…
A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of…
Quantum groupoids are a joint generalization of groupoids and quantum groups. We propose a definition of a compact quantum groupoid that is based on the theory of C*-algebras and Hilbert bimodules. The essential point is that whenever one…
A formulation of quaternionic quantum mechanics ($\mathbb{H}$QM) is presented in terms of a real Hilbert space. Using a physically motivated scalar product, we prove the spectral theorem and obtain a novel quaternionic Fourier series. After…
We study the expressive power of fragments of inclusion and independence logic defined by restricting the number k of universal quantifiers in formulas. Assuming the so-called strict semantics for these logics, we relate these fragments of…
We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…
Quantum theory's Hilbert space apparatus in its finite-dimensional version is nearly reconstructed from four simple and quantum-mechanically motivated postulates for a quantum logic. The reconstruction process is not complete, since it…
Some notes about quantum physics, an interpretation if one wishes, are put forward, insisting on `closely following the mathematics/formalism, the `nuts and bolts of what quantum physics says'. These, basically well-known, issues seem to…
We begin by discussing ``What exists?'', i.e. ontology, in Classical Physics which provided a description of physical phenomena at the macroscopic level. The microworld however necessitates a introduction of Quantum ideas for its…
We begin the study of categorical logic for continuous model theory. In particular, we 1. introduce the notions of metric logical categories and functors as categorical equivalents of a metric theory and interpretations, 2. prove a…
Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…