Related papers: The Sasaki Hook is not a [Static] Implicative Conn…
The so-called Sasaki projection was introduced by U. Sasaki on the lattice L(H) of closed linear subspaces of a Hilbert space H as a projection of L(H) onto a certain sublattice of L(H). Since L(H) is an orthomodular lattice, the Sasaki…
Abstract interpretation, Hoare logic, and incorrectness (or reverse Hoare) logic are powerful techniques for static analysis of computer programs. All of them have been successfully extended to the quantum setting, but largely developed in…
The Causal Set approach to quantum gravity asserts that spacetime, at its smallest length scale, has a discrete structure. This discrete structure takes the form of a locally finite order relation, where the order, corresponding with the…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
Causality underpins all logical reasoning. However, the causal structure in quantum processes can be far from intuitive, often differing from its classical counterpart in relativity, which is defined by the light cone. In particular, in…
Two major deviations from causality in the existing formulations of quantum mechanics, related respectively to quantum chaos and indeterminate wave reduction, are eliminated within the new, universal concept of dynamic complexity. The…
Measurement incompatibility underpins randomness generation in nonlocal phenomena. However, at its root, a more fundamental quantum feature is noncommuting (or coherent) measurements. This raises a central question: How can we operationally…
From the ancient Einstein-Podolsky-Rosen paradox to the recent Sorkin-type impossible measurements problem, the contradictions between relativistic causality, quantum non-locality, and quantum measurement have persisted. Based on quantum…
An axiomatic theory of operator connections and operator means was investigated by Kubo and Ando in 1980. A connection is a binary operation for positive operators satisfying the monotonicity, the transformer inequality and the…
In this note, we study the operation of Sasaki hook within the setting of quantum cylindric algebras by introducing cylindric quasi-implication algebras. It is first demonstrated that every quantum cylindric algebra can be converted into a…
Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Short-circuit evaluation is widely…
We consider the reversible processes between two one-to-one correlated measurement outcomes which underly both problem-solving and quantum nonlocality. In the former case the two outcomes are the setting and the solution of the problem, in…
We introduce a quantitative relational Hoare logic for quantum programs. Assertions of the logic range over a new infinitary extension of positive semidefinite operators. We prove that our logic is sound, and complete for bounded…
When a physicist performs a quantic measurement, new information about the system at hand is gathered. This paper studies the logical properties of how this new information is combined with previous information. It presents Quantum Logic as…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
Contextuality is a feature of quantum correlations. It is crucial from a foundational perspective as a nonclassical phenomenon, and from an applied perspective as a resource for quantum advantage. It is commonly defined in terms of hidden…
We consider the quantization of gravity as an SL(2,C) gauge theory in terms of Ashtekar's selfdual variables and reality conditions for the spatial metric (RCI) and its evolution (RCII). We start from a holomorphic phase space formulation.…
Quantum measurement is a fundamental concept in the field of quantum mechanics. The action of quantum measurement, leading the superposition state of the measured quantum system into a definite output state, not only reconciles…
This article presents a precise description of the interplay between the symmetries of a quantum or classical theory with spacetime interpretation, and some of its physical properties relating to causality, horizons and positive energy. Our…
A new interpretation of quantum mechanics, similar to the Copenhagen interpretation, is developed from time-symmetry arguments and commonly held principles concerning time and causality. These principles, which are grounded in ideas outside…