相关论文: Almost all classical theorems are intuitionistic

An indeterministic interpretation of classical physics has been proposed recently, in which the argument relies on attacking an alleged unwarranted metaphysical hidden assumption of the standard deterministic interpretation. This short…

Core quantum postulates including the superposition principle and the unitarity of evolutions are natural and strikingly simple. I show that -- when supplemented with a limited version of predictability (captured in the textbook accounts by…

In recent publications in physics and mathematics, concerns have been raised about the use of real numbers to describe quantities in physics, and in particular about the usual assumption that physical quantities are infinitely precise. In…

We find a translation with particularly nice properties from intuitionistic propositional logic in countably many variables to intuitionistic propositional logic in two variables. In addition, the existence of a possibly-not-as-nice…

All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…

Classical evaluations of configurations of intertwined quantum contexts induce relations, such as true-implies-false, true-implies-true, but also nonseparability among the input and output terminals. When combined, these exploitable…

Up to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic…

Canonical is a solver for type inhabitation in dependent type theory, that is, the problem of producing a term of a given type. We present a Lean tactic which invokes Canonical to generate proof terms and synthesize programs. The tactic…

It is useful to have a criterion for when the predictions of an operational theory should be considered classically explainable. Here we take the criterion to be that the theory admits of a generalized-noncontextual ontological model.…

In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…

We outline an intuitionistic view of knowledge which maintains the original Brou\-wer-Heyting-Kolmogorov semantics for intuitionism and is consistent with the well-known approach that intuitionistic knowledge be regarded as the result of…

The problem of the determinism of Quantum Mechanics has been a main one during the 20th century. At the same time, in the context of Logic and Set Theory, the importance of ancient paradoxes as well as the appearance of many new ones, has…

Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…

The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…

Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…

The representation of a Schrodinger equations as a classic Hamiltonian system allows to construct a unified perturbation theory both in classic, and in a quantum mechanics grounded on the theory of canonical transformations, and also to…

Path integral expressions for three canonical formalisms -- Ostrogradski's one, constrained one and generalized one -- of higher-derivative theories are given. For each fomalism we consider both nonsingular and singular cases. It is shown…

A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…

Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically…

I argue that scientific determinism is not supported by facts, but results from the elegance of the mathematical language physicists use, in particular from the so-called real numbers and their infinite series of digits. Classical physics…