Related papers: Fibred Coalgebraic Logic and Quantum Protocols
Functor coalgebras capture a wide range of transition systems that must however evolve in discrete steps. We introduce graded coalgebras of graded monads and propose them to model continuous-time transition systems. We develop the theory of…
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…
Structural operational semantics can be studied at the general level of distributive laws of syntax over behaviour. This yields specification formats for well-behaved algebraic operations on final coalgebras, which are a domain for the…
The framework of quantitative equational logic has been successfully applied to reason about algebras whose carriers are metric spaces and operations are nonexpansive. We extend this framework in two orthogonal directions: algebras endowed…
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and…
We summarize a new realist interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact.…
An extended analysis is made of the Gell-Mann and Hartle axioms for a generalised `histories' approach to quantum theory. Emphasis is placed on finding equivalents of the lattice structure that is employed in standard quantum logic.…
We advocates here the use of (mathematical) logic for systems biology, as a unified framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these properties. The…
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
We give an axiomatic formulation of quantum structures like semilogics and quasilogics which generalize the boolean semirings of events and fuzzy logics. The notions of distributions, states, representations observables and semiobservables…
Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…
Within the possibilistic approach to uncertainty modeling, the paper presents a modal logical system to reason about qualitative (comparative) statements of the possibility (and necessity) of fuzzy propositions. We relate this qualitative…
Quantum information and computation may serve as a source of useful axioms and ideas for the quantum logic/quantum structures project of characterizing and classifying types of physical theories, including quantum mechanics and classical…
Scalable modern-time fault-tolerant quantum computation and quantum communication in a network employ a large number of physical qubits. For example, IBM is reported to have made a 127-qubit quantum computer. Unlike classical computation,…
This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples…
The topos approach to the formulation of physical theories includes a new form of quantum logic. We present this topos quantum logic, including some new results, and compare it to standard quantum logic, all with an eye to conceptual…
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…
We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…