Notice of Retraction: Representing, managing, and reasoning about mathematical knowledge based on strong relevant logic

2008 ◽  
Author(s):  
Jing-de Cheng
Keyword(s):  
Mathematical Knowledge ◽  
Relevant Logic ◽  
Knowledge Based

Necessity, Certainty, and the A Priori

1988 ◽  
Vol 18 (1) ◽  
pp. 43-66 ◽  
Author(s):  
Albert Casullo
Keyword(s):  
Cognitive Processes ◽  
Mathematical Knowledge ◽  
A Priori ◽  
Theory Of Knowledge ◽  
A Posteriori ◽  
Unitary Theory ◽  
Knowledge Based

Empiricist theories of knowledge are attractive for they offer the prospect of a unitary theory of knowledge based on relatively well understood physiological and cognitive processes. Mathematical knowledge, however, has been a traditional stumbling block for such theories. There are three primary features of mathematical knowledge which have led epistemologists to the conclusion that it cannot be accommodated within an empiricist framework: 1) mathematical propositions appear to be immune from empirical disconfirmation; 2) mathematical propositions appear to be known with certainty; and 3) mathematical propositions are necessary. Epistemologists who believe that some nonmathematical propositions, such as logical or ethical propositions, cannot be known a posteriori also typically appeal to the three factors cited above in defending their position. The primary purpose of this paper is to examine whether any of these alleged features of mathematical propositions establishes that knowledge of such propositions cannot be a posteriori.

scholarly journals New opportunities of computer assessment of knowledge based on fractal modeling

2017 ◽  
Author(s):  
Eugeny Ivanovich Smirnov ◽  
Svetlana Dvoryatkina ◽  
Arseny Lopukhin
Keyword(s):  
Mathematical Knowledge ◽  
Cognitive Activity ◽  
Educational Process ◽  
Computer Assessment ◽  
Adaptive Training ◽  
Training Systems ◽  
Computer Monitoring ◽  
Knowledge Based ◽  
Fractal Methods

In this article the urgent problem of control systems modeling of professional competences and mathematical knowledge assessment of students is discussed. Pedagogical expediency in management of students` cognitive activity by using of new informational technologies instruments in monitoring and assessment of knowledge is proved. The possibility of fractal methods application in perfecting of the system of computer monitoring of mathematical knowledge of students as a part of the adaptive training systems is considered and realized. The design of the technology of computer monitoring of students` knowledge on the basis of fractal methods includes the following stages: development of cross-disciplinary fractal and organized base of key mathematical concepts; the creation of the expansible bank of educational and cognitive and research tasks, which is coordinated with fractal structure of the conceptual framework; the development of the program module, which is  focused on individual estimation of quality of students` educational cognitive activity in two characteristics — depth of knowledge based on the Hurst exponent and the size of synergetic effect of educational cognitive activity. The software realization of technology of the computerized control of training in mathematical disciplines quality as a part of the adaptive training system is enabled in the programming language C#. The experience of implementation and operation of the controlling systems realized in the adaptive training systems based on the fractal model operation showed reliability of their work and allowed to increase the quality of educational process management and its effectiveness in general. Using of fractal techniques in computer assessment of mathematical knowledge of students makes it possible to increase the accuracy and speed of evaluation of the students` knowledge.

scholarly journals Introducing MathQA: a Math-Aware question answering system

2018 ◽  
Vol 46 (4) ◽  
pp. 214-224 ◽  
Author(s):  
Moritz Schubotz ◽  
Philipp Scharpf ◽  
Kaushal Dudhat ◽  
Yash Nagar ◽  
Felix Hamborg ◽  
...  
Keyword(s):  
Mathematical Knowledge ◽  
Design Methodology ◽  
Question Answering ◽  
User Study ◽  
Content Type ◽  
Question Answering System ◽  
Knowledge Based ◽  
Natural Language Question ◽  
Language Question

Purpose This paper aims to present an open source math-aware Question Answering System based on Ask Platypus. Design/methodology/approach The system returns as a single mathematical formula for a natural language question in English or Hindi. These formulae originate from the knowledge-based Wikidata. The authors translate these formulae to computable data by integrating the calculation engine sympy into the system. This way, users can enter numeric values for the variables occurring in the formula. Moreover, the system loads numeric values for constants occurring in the formula from Wikidata. Findings In a user study, this system outperformed a commercial computational mathematical knowledge engine by 13 per cent. However, the performance of this system heavily depends on the size and quality of the formula data available in Wikidata. As only a few items in Wikidata contained formulae when the project started, the authors facilitated the import process by suggesting formula edits to Wikidata editors. With the simple heuristic that the first formula is significant for the paper, 80 per cent of the suggestions were correct. Originality/value This research was presented at the JCDL17 KDD workshop.

scholarly journals Comparing mathematics knowledge of first-year students from three different school curricula

2018 ◽  
Vol 115 (1/2) ◽  
Author(s):  
Sonica Froneman ◽  
Mariette Hitge
Keyword(s):  
Traditional Knowledge ◽  
Mathematical Knowledge ◽  
Engineering Students ◽  
National Curriculum ◽  
First Year ◽  
First Year Students ◽  
Knowledge Based ◽  
Student Cohorts ◽  
Mathematics Knowledge ◽  
School Curricula

Mathematics forms an integral part in the training of scientists and engineers. In recent history the South African school system has experienced several changes in school curricula. In 1994 the traditional knowledge-based curricula were replaced by an outcomes-based curriculum. Owing to implementation problems which resulted in resistance from teachers and the general public, revisions followed of which the National Curriculum Statement (NCS) and Curriculum Assessment Policy Statements had the most direct effect in terms of preparation for tertiary mathematics. We report here on an investigation of the basic mathematical knowledge of three student cohorts representing three curricula, namely the last cohort that received the traditional knowledge-based curriculum, and the first cohorts that received the two outcomes-based curricula. The results indicate that changes in the mathematical content of the curricula did not impact negatively on the basic mathematical knowledge of students enrolled for tertiary mainstream mathematics. The only exception is Euclidean geometry, for which certain topics were transferred to an optional paper in the NCS curriculum. Significance: • The introduction of outcomes-based curricula in South Africa initiated a discourse on the preparedness of first-year students for programmes with mainstream mathematics. • The availability of a homogeneous set of samples and a uniform test provided a unique opportunity to compare the basic mathematical knowledge of first-year natural science and engineering students entering university from three different exit-level school curricula.

Is the Personal Always Political?

2017 ◽  
Vol 38 (3) ◽  
pp. 133-143 ◽  
Author(s):  
Danny Osborne ◽  
Yannick Dufresne ◽  
Gregory Eady ◽  
Jennifer Lees-Marshment ◽  
Cliff van der Linden
Keyword(s):  
Survey Data ◽  
National Survey ◽  
Negative Relationship ◽  
Openness To Experience ◽  
Political Sophistication ◽  
Knowledge Based

Abstract. Research demonstrates that the negative relationship between Openness to Experience and conservatism is heightened among the informed. We extend this literature using national survey data (Study 1; N = 13,203) and data from students (Study 2; N = 311). As predicted, education – a correlate of political sophistication – strengthened the negative relationship between Openness and conservatism (Study 1). Study 2 employed a knowledge-based measure of political sophistication to show that the Openness × Political Sophistication interaction was restricted to the Openness aspect of Openness. These studies demonstrate that knowledge helps people align their ideology with their personality, but that the Openness × Political Sophistication interaction is specific to one aspect of Openness – nuances that are overlooked in the literature.

Connectives Increase Knowledge-Based Inferences

1994 ◽  
Author(s):  
Gregory Barker ◽  
Keith Millis ◽  
Jonathan M. Golding
Keyword(s):  
Knowledge Based

The contribution of low-level sensory features versus knowledge-based factors for encoding of objects in working memory

2013 ◽  
Author(s):  
Valerio Santangelo ◽  
Simona Arianna Di Francesco ◽  
Serena Mastroberardino ◽  
Emiliano Macaluso
Keyword(s):  
Working Memory ◽  
Low Level ◽  
Knowledge Based ◽  
Sensory Features
Sign in / Sign up

Export Citation Format

Share Document