相关论文: Undecidability everywhere?

This article addresses the question of when physical laws and their consequences can be computed. If a physical system is capable of universal computation, then its energy gap can't be computed. At an even more fundamental level, the most…

In a recent paper [1], it has been claimed that the outcomes of a quantum coin toss which is idealized as an infinite binary sequence is 1-random. We also defend the correctness of this claim and assert that the outcomes of quantum…

It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…

We establish the undecidability of conditional affine information inequalities, the undecidability of the conditional independence implication problem with a constraint that one random variable is binary, and the undecidability of the…

In light of G\"{o}del's undecidability results (incomplete theorems) for math, quantum indeterminism indicates that physics and the Universe may be indeterministic, incomplete, and open in nature, and therefore demand no single unification…

It is a widespread belief that results like G\"odel's incompleteness theorems or the intrinsic randomness of quantum mechanics represent fundamental limitations to humanity's strive for scientific knowledge. As the argument goes, there are…

We investigate the problem of deciding whether a system of linear equations, together with divisibility conditions on the variables, has a solution over holomorphy subrings of global fields. We obtain decidability results when we allow…

One main goal of argumentation theory is to evaluate arguments and to determine whether they should be accepted or rejected. When there is no clear answer, a third option, being undecided, has to be taken into account. Indecision is often…

Using recent machine learning results that present an information-theoretic perspective on underfitting and overfitting, we prove that deciding whether an encodable learning algorithm will always underfit a dataset, even if given unlimited…

The conditions under which, the continuity equation can be substituted by an ordinary non differential equation, will be discussed. Since continuity equation is a fundamental equation, this result will be applicable in a vast area of…

Interpretability and explainability have gained more and more attention in the field of machine learning as they are crucial when it comes to high-stakes decisions and troubleshooting. Since both provide information about predictors and…

In this note we give a negative answer to Abraham Robinson's question whether a finitely generated extension of an undecidable field is always undecidable. We construct 'natural' undecidable fields of transcendence degree 1 over Q all of…

The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…

We point out that some questions in quantum field theory are undecidable in a precise mathematical sense. More concretely, it will be demonstrated that there is no algorithm answering whether a given 2d supersymmetric Lagrangian theory…

We prove undecidability for every positive relevant logic extending the system axiomatized by hypothetical syllogism, prefixing, and suffixing and contained in the logic of the semilattice frame $(P_{\mathrm{fin}}(\mathbb{N}), \cup,…

We study infinite two-player games where one of the players is unsure about the set of moves available to the other player. In particular, the set of moves of the other player is a strict superset of what she assumes it to be. We explore…

There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Go\"edel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things…

Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action…

Spacetime singularities in general relativity are commonly thought to be problematic, in that they signal a breakdown in the theory. We address the question of how to interpret this breakdown, restricting our attention to classical…

Some possible (re)sources of indeterminism and randomness encountered in physics are enumerated. These gaps in the physical laws, if they exist, could possibly be exploited for dualistic interfaces. We also speculate that physical laws and…