A Mathematical Theory of Hints

1995 ◽  
Author(s):  
Jürg Kohlas ◽  
Paul-André Monney
Keyword(s):  
Mathematical Theory

Evaluation Opportunities in Mechanized Theories

10.29007/7kx8 ◽  
2018 ◽  
Author(s):  
Joe Hurd
Keyword(s):  
Mathematical Theory ◽  
Theorem Prover ◽  
Mechanized Mathematics ◽  
Reasoning Tasks

This invited talk will look at logic solvers through the application lens of constructing and processing a theory library of mechanized mathematics. In fact, constructing and processing theories are two distinct applications, and each will be considered in turn. Construction is carried out by formalizing a mathematical theory using an interactive theorem prover, and logic solvers can remove much of the drudgery by automating common reasoning tasks. At the theory library level, logic solvers can provide assistance with theory engineering tasks such as compressing theories, managing dependencies, and constructing new theories from reusable theory components.

Mathematical Theory of Neural Networks

2000 ◽  
Author(s):  
Eduardo D. Sontag ◽  
Hector J. Sussman
Keyword(s):  
Neural Networks ◽  
Mathematical Theory

PIOPLE. INFORMATION. DEGRADATION

2019 ◽  
pp. 44-53
Author(s):  
Andrey Varlamov ◽  
Vladimir Rimshin
Keyword(s):  
Information Theory ◽  
Mathematical Theory ◽  
Maximum Information ◽  
Building Models ◽  
Man And Nature ◽  
History Of ◽  
Nature And Society ◽  
Relationship Of ◽  
Link Information ◽  
The Relationship

Considered the issues of interaction between man and nature. Noted that this interaction is fundamental in the existence of modern civilization. The question of possible impact on nature and society with the aim of preserving the existence of human civilization. It is shown that the study of this issue goes towards the crea-tion of models of interaction between nature and man. Determining when building models is information about the interaction of man and nature. Considered information theory from the viewpoint of interaction between nature and man. Noted that currently information theory developed mainly as a mathematical theory. The issues of interaction of man and nature, the availability and existence of information in the material sys-tem is not studied. Indicates the link information with the energy terms control large flows of energy. For con-sideration of the interaction of man and nature proposed to use the theory of degradation. Graphs are pre-sented of the information in the history of human development. Reviewed charts of population growth. As a prediction it is proposed to use the simplest based on the theory of degradation. Consideration of the behav-ior of these dependencies led to the conclusion about the existence of communication energy and information as a feature of the degradation of energy. It justifies the existence of border life ( including humanity) at the point with maximum information. Shows the relationship of energy and time using potential energy.

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