Proving in Mathematics Education – On the Proof using ATP

2019 ◽  
pp. 558-563
Author(s):  
Tadashi Takahashi
Keyword(s):  
Mathematics Education ◽  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Mathematical Thinking ◽  
Present Situation ◽  
Point Of View ◽  
Clear Vision ◽  
Euclid’S Elements ◽  
A Chain

The aim of the mathematics education is the acquisition of “knowledge/skill of the mathematics” and “the mathematical thinking”. Proving is a chain of the logic in mathematics and is “mathematical thinking” itself. So, proving is the domain that is important from a point of view that can evaluate the acquisition of enough “mathematical thinking”. There is a variety of sense of values in the present situation of the proof using the ATP (Automated theorem proving). We should establish a clear vision as mathematics education in this situation. That is, in mathematics education, we should build sense of values for proof using the ATP newly. To that end, we fix contents of the mathematics, and it is necessary to prove them by using ATP. We would like to assume the aim the theorems of Euclid's Elements. Because the contents are the basics of the mathematical thinking. The proving is an important aim in the mathematics education, it is necessary to clarify new value by using the ATP as mathematics education.

scholarly journals Challenge to the proving of theorems of Euclid's elements of as ATP

2019 ◽  
Vol 3 (4) ◽  
pp. 9-13
Author(s):  
Keyword(s):  
Mathematical Logic ◽  
Mathematics Education ◽  
Theorem Proving ◽  
Automated Reasoning ◽  
Automated Theorem Proving ◽  
Euclidean Geometry ◽  
Proof Assistant ◽  
Weak Point ◽  
Euclid’S Elements ◽  
Generic Proof

Automated theorem proving (ATP) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. An Isabelle/HOL is a generic proof assistant. We perform the challenge for the proving theorems of Euclid's elements of geometry. We could prove some theorems of Euclid's elements of geometry. Technique of programing and mental conception interact. The mathematics education which prove theorems of the Euclidean geometry by using the Isabelle/HOL can correct the present weak point

One Point of View: Tracking Is Inconsistent with the Standards

1989 ◽  
Vol 36 (8) ◽  
pp. 6
Author(s):  
Judy Mumme
Keyword(s):  
Mathematics Education ◽  
Mathematics Instruction ◽  
Point Of View ◽  
School Mathematics ◽  
Nctm Standards ◽  
Clear Vision

The NCTM Standards (Commission on Standards of School Mathematics of the NCTM 1987) articulate a clear vision for mathematics education, containing the central ideas of mathemat ics we wish all students to understand. Achieving the fundamental changes these Standards envision will require educators to reexamine many existing practices. Efforts to improve mathematics instruction interface with the broader issues facing education.

Do Event-Related Brain Potentials Reflect Mental (Cognitive) Operations?

2002 ◽  
Vol 16 (3) ◽  
pp. 129-149 ◽  
Author(s):  
Boris Kotchoubey
Keyword(s):  
Cognitive Processes ◽  
Point Of View ◽  
Internal Variables ◽  
Brain Potentials ◽  
Cognitive Operations ◽  
External Variables ◽  
Series Of Experiments ◽  
Mental Operations ◽  
A Chain ◽  
Processing Mechanisms

Abstract Most cognitive psychophysiological studies assume (1) that there is a chain of (partially overlapping) cognitive processes (processing stages, mechanisms, operators) leading from stimulus to response, and (2) that components of event-related brain potentials (ERPs) may be regarded as manifestations of these processing stages. What is usually discussed is which particular processing mechanisms are related to some particular component, but not whether such a relationship exists at all. Alternatively, from the point of view of noncognitive (e. g., “naturalistic”) theories of perception ERP components might be conceived of as correlates of extraction of the information from the experimental environment. In a series of experiments, the author attempted to separate these two accounts, i. e., internal variables like mental operations or cognitive parameters versus external variables like information content of stimulation. Whenever this separation could be performed, the latter factor proved to significantly affect ERP amplitudes, whereas the former did not. These data indicate that ERPs cannot be unequivocally linked to processing mechanisms postulated by cognitive models of perception. Therefore, they cannot be regarded as support for these models.

The 10th IJCAR automated theorem proving system competition – CASC-J10

2021 ◽  
pp. 1-15
Author(s):  
Geoff Sutcliffe
Keyword(s):  
Theorem Proving ◽  
Classical Logic ◽  
Automated Theorem Proving ◽  
Fully Automatic

The CADE ATP System Competition (CASC) is the annual evaluation of fully automatic, classical logic Automated Theorem Proving (ATP) systems. CASC-J10 was the twenty-fifth competition in the CASC series. Twenty-four ATP systems and system variants competed in the various competition divisions. This paper presents an outline of the competition design, and a commentated summary of the results.

Retrieval System and Dynamic Algorithm Looking for Axioms of Notions Defined by Programs

1993 ◽  
Vol 19 (3-4) ◽  
pp. 275-301
Author(s):  
Andrzej Biela
Keyword(s):  
Theorem Proving ◽  
Dynamic Process ◽  
Functional Equations ◽  
Automated Theorem Proving ◽  
Retrieval System ◽  
Formal System ◽  
Dynamic Algorithm ◽  
Algorithmic Logic ◽  
Correctness Of Programs

In this paper we shall introduce a formal system of algorithmic logic which enables us to formulate some problems connected with a retrieval system which provides a comprehensive tool in automated theorem proving of theorems consisting of programs, procedures and functions. The procedures and functions may occur in considered theorems while the program of the above mentioned system is being executed. We can get an answer whether some relations defined by programs hold and we can prove functional equations in a dynamic way by looking for a special set of axioms /assumptions/ during the execution of system. We formulate RS-algorithm which enables us to construct the set of axioms for proving some properties of functions and relations defined by programs. By RS-algorithm we get the dynamic process of proving functional equations and we can answer the question whether some relations defined by programs hold. It enables us to solve some problems concerning the correctness of programs. This system can be used for giving an expert appraisement. We shall provide the major structures and a sketch of an implementation of the above formal system.

scholarly journals Study of Human and Robot Social Interaction Using Artificial Cognition Methods

2020 ◽  
pp. 458-464
Author(s):  
Rupal Chaudhary
Keyword(s):  
Social Interaction ◽  
Control Systems ◽  
Mathematical Thinking ◽  
Point Of View ◽  
Wide Scope ◽  
Long Run ◽  
Normal Human ◽  
Express Information ◽  
The Individual ◽  
Human Robot Collaboration

Abstract. HRI challenges AI in numerous regards: dynamic, somewhat obscure conditions that were not initially intended for robots; a wide scope of circumstances with rich semantics to comprehend and decipher; physical associations with people that require fine, low-inactivity, yet socially satisfactory control systems; regular and multimodal correspondence. This paper is an endeavor to describe these difficulties and to introduce a lot of key dynamic issues that should be tended to for an intellectual robot to effectively impart space and assignments to a person. To begin with, we distinguish the individual and community oriented intellectual aptitudes required: mathematical thinking and circumstance appraisal dependent on point of view taking and cost-adequacy investigation; securing and the article talks about every one of these capacities, presents work executions and shows how they consolidate in a sound and unique human-robot collaboration deliberative design. Fortified by the aftereffects of the preliminary, we should in the long run exhibit how the board's express information, both symbolic and quantitative, is instrumental to more extravagant and more normal human-robot associations by squeezing for certain, human-level semantics inside the robot framework.

Verifying B proof rules using deep embedding and automated theorem proving

2013 ◽  
Vol 14 (1) ◽  
pp. 101-119 ◽  
Author(s):  
Mélanie Jacquel ◽  
Karim Berkani ◽  
David Delahaye ◽  
Catherine Dubois
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Proof Rules ◽  
Deep Embedding
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