Related papers: The space of logically consistent classical proces…

Causal knowledge is vital for effective reasoning in science, as causal relations, unlike correlations, allow one to reason about the outcomes of interventions. Algorithms that can discover causal relations from observational data are based…

A model of a discrete pregeometry on a microscopic scale is introduced. This model is a finite network of finite elementary processes. The mathematical description is a d-graph that is a generalization of a graph. This is the particular…

Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…

Recently, the possible existence of quantum processes with indefinite causal order has been extensively discussed, in particular using the formalism of process matrices. Here we give a new perspective on this question, by establishing a…

One can often encounter claims that classical (Kolmogorovian) probability theory cannot handle, or even is contradicted by, certain empirical findings or substantive theories. This note joins several previous attempts to explain that these…

With recent advances in natural language processing, rationalization becomes an essential self-explaining diagram to disentangle the black box by selecting a subset of input texts to account for the major variation in prediction. Yet,…

Using a simple probabilistic model, we illustrate that a small part of a strongly correlated many-body classical system can show a paradoxical behavior, namely asymptotic stochastic independence. We consider a triangular array such that…

Bell inequalities limit the possible observations of non-communicating parties. Here, we present analogous inequalities for any number of communicating parties under the causal constraints of static causal order, definite causal order, and…

Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…

From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…

We demonstrate exciting similarities between classical and quantum many body systems whose microscopic dynamics are composed of non-reciprocal three-site facilitated exclusion processes. We show that the quantum analogue of the classical…

Inspired by a quantum mechanical formalism to model concepts and their disjunctions and conjunctions, we put forward in this paper a specific hypothesis. Namely that within human thought two superposed layers can be distinguished: (i) a…

Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…

Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate…

Discovery of causal relations is fundamental for understanding the dynamics of complex systems. While causal interactions are well defined for acyclic systems that can be separated into causally effective subsystems, a mathematical…

Three paradigms commonly used in classical, pre-quantum physics to describe particles (that is: the material point, the test-particle and the diluted particle (droplet model)) can be identified as limit-cases of a quantum regime in which…

A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…

The research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on. Without these assumptions the sequences of…

Many tasks in statistical and causal inference can be construed as problems of \emph{entailment} in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for \emph{causal}…