Related papers: Embracing undecidability: Cognitive needs and theo…

We warn against a common but incomplete understanding of empirical research in machine learning that leads to non-replicable results, makes findings unreliable, and threatens to undermine progress in the field. To overcome this alarming…

We review recent work that employs the framework of logical inference to establish a bridge between data gathered through experiments and their objective description in terms of human-made concepts. It is shown that logical inference…

This paper makes a first step towards a logic of learning from experiments. For this, we investigate formal frameworks for modeling the interaction of causal and (qualitative) epistemic reasoning. Crucial for our approach is the idea that…

A central paradigm behind process semantics based on observability and testing is that the exact moment of occurring of an internal nondeterministic choice is unobservable. It is natural, therefore, for this property to hold when the…

Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…

Physical theories must stem from observation. The possibility that perceived events are simulated, not real, raises a crucial dilemma about the credibility of known physics, known as the simulation hypothesis. To analyze this hypothesis in…

At any time, there are areas of science where we are standing at the frontier of knowledge, and can wonder whether we have reached a fundamental limit to human understanding. What is ultimately possible in physics? I will argue here that it…

A theory of everything should not only tell us the laws for matter, gravity, and possibly boundary condition for the universe. In addition, it should specify the relation between theory and experience. Here I argue for a minimal…

The ability to make decisions based on data, with its inherent uncertainties and variability, is a complex and vital skill in the modern world. The need for such quantitative critical thinking occurs in many different contexts, and while it…

Free will discourse is primarily centred around the thesis of determinism. Much of the literature takes determinism as its starting premise, assuming it true for the sake of discussion, and then proceeds to present arguments for why, if…

The epistemological interpretation of quantum mechanics is still in an unacceptable status. This becomes obvious if looking on the variety of interpretations currently under discussion. However, the physical community together with…

Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum…

We lay the groundwork for a formal framework that studies scientific theories and can serve as a unified foundation for the different theories within physics. We define a scientific theory as a set of verifiable statements, assertions that…

Whenever a mathematical proposition to be proved requires more information than it is contained in an axiomatic system, it can neither be proved nor disproved, i.e. it is undecidable, or logically undetermined, within this axiomatic system.…

Recent work has examined how undecidable problems can arise in quantum information science. We augment this by introducing three new undecidable problems stated in terms of tensor networks. These relate to ideas of Penrose about the…

Our manuscript studies linear temporal (with UNTIL and NEXT) logic based at a conception of intransitive time. non-transitive time. In particular, we demonstrate how the notion of knowledge might be represented in such a framework (here we…

A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…

General relativity, despite its profound successes, fails as a complete theory due to presence of singularities. While it is widely believed that quantum gravity has the potential to be a complete theory, in which spacetime consistently…

In the present article we use the quantum formalism to describe the process of choice under rational ignorance. We consider as a basic task a question or an issue where the only answers are 0 and 1. We show that under rational ignorance the…

After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…