Related papers: Restricted Complexity, General Complexity
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
By using ideas on complexity and randomness originally suggested by the mathematician-philosopher Gottfried Leibniz in 1686, the modern theory of algorithmic information is able to show that there can never be a "theory of everything" for…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
Motivated by description logics, we investigate what happens to the complexity of modal satisfiability problems if we only allow formulas built from literals, $\wedge$, $\Diamond$, and $\Box$. Previously, the only known result was that the…
Computational complexity has often been ignored in philosophy of mind, in philosophical artificial intelligence studies. The purpose of this paper is threefold. First and foremost, to show the importance of complexity rather than…
A major challenge of interdisciplinary description of complex system behaviour is whether real systems of higher complexity levels can be understood with at least the same degree of objective, "scientific" rigour and universality as…
I consider the isolation of general relativity research from the rest of theoretical physics during the 1930s-1950s, and the subsequent reinvigoration of the field. I suggest that the main reason for the isolation was that relativists of…
In this comprehensive review, we describe a new mathematical problem in artificial intelligence (AI) from a mathematical modeling perspective, following the philosophy stated by Rudolf E. Kalman that "Once you get the physics right, the…
The study of Complex Systems is considered by many to be a new scientific field, and is distinguished by being a discipline that has applications within many separate areas of scientific study. The study of Neural Networks, Traffic…
Numerous definitions for complexity have been proposed over the last half century, with little consensus achieved on how to use the term. A definition of complexity is supplied here that is closely related to the Kolmogorov Complexity and…
Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and computational complexity theory -- in the discrete setting of bits and Turing machines. Over real numbers, on the other hand, the…
The quantified constraint satisfaction problem (QCSP) is a powerful framework for modelling computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
We propose a tractable unified framework to study the evolution and interaction of model-misspecification concerns and complexity aversion in repeated decision problems. This aims to capture environments where decision makers worry that…
It is not known what the limitations are on using quantum computation to speed up classical computation. An example would be the power to speed up PSPACE-complete computations. It is also not known what the limitations are on the duration…
There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…
Complex systems and their underlying convoluted networks are ubiquitous, all we need is an eye for them. They pose problems of organized complexity which cannot be approached with a reductionist method. Complexity science and its emergent…
Constraint propagation is one of the techniques central to the success of constraint programming. To reduce search, fast algorithms associated with each constraint prune the domains of variables. With global (or non-binary) constraints, the…
Entropy always increases monotonically in a closed system but complexity increases at first and then decreases as equilibrium is approached. Commonsense information-related definitions for entropy and complexity demonstrate that complexity…