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In this thesis, we will look at some known and some previously uninvestigated notions of effective undecidability. We try to discover how far we can stretch effective undecidability in the hope to get a more tractable solution to Post's…
An interaction is a certain symmetric graph that describes the possible transition of states of adjacent sites of large-scale interacting systems. In the series of studies Bannai-Kametani-Sasada arXiv:2009.04699, Bannai-Sasada…
Gibbs paradox in the context of statistical mechanics addresses the issue of additivity of entropy of mixing gases. The usual discussion attributes the paradoxical situation to classical distinguishability of identical particles and credits…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…
I apply some of the lessons from quantum theory, in particular from Bell's theorem, to a debate on the foundations of decision theory and causation. By tracing a formal analogy between the basic assumptions of Causal Decision Theory…
Solving the fundamental and optical gap problems, which yield information about charged and neutral excitations in electronic systems, is one of the biggest challenge in density-functional theory (DFT). Despite their intrinsic difference,…
We address the decision problem for a fragment of real analysis involving differentiable functions with continuous first derivatives. The proposed theory, besides the operators of Tarski's theory of reals, includes predicates for…
We show that for an infinite, uniformly charged plate no well defined electric field exists in the framework of electrostatics, because it cannot be defined as a mathematically consistent limit of a solution for a finite plate. We discuss…
The 20th century has revealed two important limitations of scientific knowledge. On the one hand, the combination of Poincar\'e's nonlinear dynamics and Heisenberg's uncertainty principle leads to a world picture where physical reality is,…
A unified treatment for the existence of free energy in several random energy models is presented. If the sequence of distributions associated with the particle systems obeys a large deviation principle, then the free energy exists almost…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
Rather than discussing the isolated merits of a nominative theory of uncertainty, this paper focuses on a class of problems, referred to as Dynamic Classification Problem (DCP), which requires the integration of many theories, including a…
Orbit determination is possible for a chaotic orbit of a dynamical system, given a finite set of observations, provided the initial conditions are at the central time. In a simple discrete model, the standard map, we tackle the problem of…
We introduce a qubit-based version of the quantum switch, consisting in a variation of the Fermi problem. Two qubits start in a superposition state where one qubit is excited and the other in the ground state, but it is undefined which is…
The Principle of Sufficient Reason implies determinism. An explicit indeterministic quantum jump dynamics is constructed, which may be naturally transformed into a deterministic one. A consistent application of the Principle of Sufficient…
The uncertainty principle is often interpreted by the tradeoff between the error of a measurement and the consequential disturbance to the followed ones, which originated long ago from Heisenberg himself but now falls into reexamination and…
Quantum theory, despite its remarkable success, struggles to represent certain experimental data, particularly those involving integer functions and deterministic relations between quantum jumps. We address this limitation by proposing a…
Controversy about the significance of underdetermination of theories persists in the philosophy and conduct of science. The issue has practical import when research is used to inform decision making, because scientific uncertainty yields…
The most important characteristics of the fragmentation of heterogeneous solids is that the mass (size) distribution of pieces is described by a power law functional form. The exponent of the distribution displays a high degree of…