The …rst serious attack to the theoretical propositions and policy implications put forward by the "neoclassical synthesis" is due to Milton Friedman (1968) and Edmund Phelps (1967). At the end of the 1960s, they independently developed similar ideas aimed at explaining the positive correlation between output ‡uctuations and in‡ation in the short-run, preserving the neoclassical property of lon...

The author has submitted to Mizar Mathematical Library a series of five articles introducing a framework for the formalization of classical first-order model theory. In them, Gödel’s completeness and Lowenheim-Skolem theorems have also been formalized for the countable case, to offer a first application of it and to showcase its utility. This is an overview and commentary on some key aspects of...

Spring algorithms are regarded as eeective tools for visualizing undirected graphs. One major feature of applying spring algorithms is to display symmetric properties of graphs. This feature has been connrmed by numerous experiments. In this paper, rstly we formalize the concepts of graph symmetries in terms of \reeectional" and \rotational" automorphisms; and characterize the types of symmetri...

In this article we formalize some number theoretical algorithms, Euclidean Algorithm and Extended Euclidean Algorithm [9]. Besides the a gcd b, Extended Euclidean Algorithm can calculate a pair of two integers (x, y) that holds ax + by = a gcd b. In addition, we formalize an algorithm that can compute a solution of the Chinese remainder theorem by using Extended Euclidean Algorithm. Our aim is ...

I attempt to demonstrate that the concept of institutional fit and the closely related approach of institutional diagnosis can be improved with the process of formalization. In this context, the concept of fit is interpreted as a way of expressing certain theoretical propositions that relate a set of variables with each other and with an outcome. This perspective is demonstrated through the use...

Human thought, perception, reasoning, and problem solving are highly dependent on causal inferences. This paper presents a set of cognitive models for causation analyses and causal inferences. The taxonomy and mathematical models of causations are created. The framework and properties of causal inferences are elaborated. Methodologies for uncertain causal inferences are discussed. The theoretic...

Deep learning has had a profound impact on computer science in recent years, with applications to image recognition, language processing, bioinformatics, and more. Recently, Cohen et al. provided theoretical evidence for the superiority of deep learning over shallow learning. We formalized their mathematical proof using Isabelle/HOL. The Isabelle development simplifies and generalizes the origi...

We propose a formalization of analog algorithms, extending the framework of abstract state machines to continuous-time models of computation. The states of ‘continuous’ machinery . . . form a continuous manifold, and the behaviour of the machine is described by a curve on this manifold. All machinery can be regarded as continuous, but when it is possible to regard it as discrete it is usually b...