The book A Generative Theory of Shape (Michael Leyton, Springer-Verlag, 2001) develops new foundations for geometry specifically designed to give a single mathematical language for the enormous range of information objects involved in the product lifecycle. This is done by giving a mathematical theory of the structure of intelligently-generated objects. It is argued that intelligence is charact...

This paper investigates the foundation of rnaxipnin, one of the central qualitative decision criteria, using the approach taken by Savage (Savage 1972) to investigate the foundation and rationality of classical decision theory. This approach asks “which behaviors could result from the use of a particular decision procedure?” The answer to this question provides two important insights: (1) under...

This text consists of additions to the book “Foundations of Garside Theory”, EMS Tracts in Mathematics, vol. 22 (2015)—see introduction and table of contents in arXiv:1309.0796—namely skipped proofs and solutions to selected exercises.

Like Humpty Dumpty, many philosophers take pride in saying what they mean and meaning what they say. Literalism does have its virtues, like when you're drawing up a contract or programming a computer, but generally we prefer to speak loosely and leave a lot to inference. Language works far more efficiently that way. Two Kinds of Looseness It helps if you can rely on people not to take you too l...

9/26/2017 Two very small edits after reading through the entire document. Made these version notes tiny. 6/14/2017 Tidied up the description of the inductive argument for coincidence of notions of symmetry. X is an element not a subset of P(clan[A]) in that argument. 6/10/2017 corrected the application of the induction in the extension property proof to the better form in the last submitted ver...

The paper aims to demonstrate that category theory (CT) methods are appropriate in the model management context. We show that CT naturally appears on stage, when we model such basic constructs as model merge and parallel composition accurately and consistently. We present categorical constructs in a tutorial-like style by applying them to simple labeled transition systems (LTSs), and reveal new...

This review covers the main aspects of black hole accretion disk theory. We begin with the view that one of the main goals of the theory is to better understand the nature of black holes themselves. In this light we discuss how accretion disks might reveal some of the unique signatures of strong gravity: the event horizon, the innermost stable circular orbit, and the ergosphere. We then review,...

This article reconsiders the Harsanyi–Sen debate concerning whether Harsanyi is justified in interpreting his Aggregation and Impartial Observer Theorems as providing axiomatizations of utilitarianism. Sen’s criticism and its formalization by Weymark are based on the claim that von Neumann–Morgenstern utility theory is ordinal, whereas Harsanyi’s utilitarian conclusions require cardinal utility...

1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2: Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3: The Classical Sequent Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

The question how and why mathematical probability theory can be applied to the “real world” has been debated for centuries. We try to survey the role of algorithmic information theory (Kolmogorov complexity) in this debate. 1 Probability theory paradox One often describes the natural sciences framework as follows: a hypothesis is used to predict something, and the prediction is then checked aga...