• The Mathematical Education
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• v.38 no.2
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• pp.159-164
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• 1999

The purpose of this paper is to find role of in and logic in creative problem solving process. Intuition and logic have played an important role in creative problem solving process. Nevertheless, Intuition has been treated less importantly than logic. Therefore, I intend to review the role of intuition, and then the relationship of intuition and logic, and the role of intuition and logic in creative problem solving process. Although intuition gives an important clue in problem solving process, it may sometimes cause an error. This fact gives an idea that intuition and logic have to be harmoniously cultivated. In fact, Intuition and logic have been playing a complementary role in creative problem solving process. A creative learner is regarded as a mathematician of his age. It must be through intuition and logic that he/she solves the problem creatively, just as a mathematician invents the new mathematical fact through unconscious and conscious process. In this respective, teachers also should make every effort to cultivate intuition and logic themselves.

• Journal for History of Mathematics
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• v.21 no.1
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• pp.17-28
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• 2008

This Paper introduces a historical background of mathematical logic. Logic and mathematics were not developed dependently until the mid of the nineteenth century, when two streams of logic and mathematics came to form a river so that brought forth synergy effects. Since the mid-nineteenth century mathematization of logic were proceeded while attempts to reduce mathematics to logic were made. Against this background $G{\ddot{o}}del's$ proof shows the limitation of formalism by proving that there are true arithmetical propositions that are not provable.

• Journal for History of Mathematics
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• v.34 no.6
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• pp.195-204
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• 2021

Mathematical induction is one of the deductive methods used for proving mathematical theorems, and also used as an inductive method for investigating and discovering patterns and mathematical formula. Proper understanding of the mathematical induction provides an understanding of deductive logic and inductive logic and helps the developments of algorithm and data science including artificial intelligence. We look at the origin of mathematical induction and its usage and educational aspects.

• Journal for History of Mathematics
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• v.35 no.2
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• pp.43-56
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• 2022

The 21st century world has experienced all-around changes from the 4th industrial revolution. In this developmental changes, artificial intelligence is at the heart, with data science adopting certain scientific methods and tools on data. It is necessary to investigate on the logic lying underneath the methods and tools. We look at the origins of logic, deduction and induction, and scientific methods, together with mathematical induction, probabilistic method and data science, and their meaning.

• Journal for History of Mathematics
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• v.25 no.1
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• pp.57-70
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• 2012

We will research the elementary formal logic and mathematical concept represented in Mojing, and focus on the ancient Chinese's mathematical principles implicit in Mojing. Moreover, the mathematical significance and values of Mojing are examined.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.803-808
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• 1994

Since L$\ddot{o}$b's announcement of his solution to Henkin's problem (L$\ddot{o}$b (1954, 1955)) there has been successful and fruitful research on provability logic tied up with modal logic. Specially, L$\ddot{o}$b's Theorem is of far-reaching significance in the following meta-mathematical and philosophical sense.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.61-71
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• 2011

The notion of a complicated pre-logic is introduced and investigated some properties of it. A special set in a pre-logic is established and some related its properties are discussed. Also more extended special sets in a pre-logic are introduced and some relations with deductive systems are obtained.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.111-119
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• 1999

This paper discusses jLogic, a mathematical logic education software developed by the author. jLogic is basically a MS-Windows based software that can construct first-order models, formulas and thet their satisfiablity. Logical formulas are easily input by a "keyboard" maintained by jLogic. A special finite model, called the "Toy World" can be visually cinstructed and modified. The user is supposed to answer the following 3 questions about the selected logical expression: 1. Is it a grammatically correct logical formula? 2. Is it a sentence that has a definite truth value? 3. Is th sentence true or false? When the user inputs his answer in the "Inspector window" and then presses the OK button, jLogic instantly tests the validity of the answer and tells the user the result. jLogic is freely downloaded from http://gauss.kyungpook.ac.kr/~jlogic/

• Research in Mathematical Education
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• v.12 no.3
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• pp.201-213
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• 2008

The main purpose of this study is to explore the relationship between the 'logical reasoning skill' and performance in the logic unit that is part of the grade 9 syllabus in mathematics in Turkey. After the teaching of the logic unit, an achievement test, a general skills test and the test of logical reasoning were administered to the 80, 9th year high school students. Pearson Moments Correlation coefficient was used for the analysis of the data to determine the relations between the variables. In addition to that to obtain the most suitable regression explaining the students' performances in the logic unit, stepwise multiple regressions analysis was used. At the end of the study, statistically significant relations were found between the students' performance in the logic unit and their logical reasoning skills, their results of the shape recognition test from the general skills battery and their overall performance in the mathematics lesson.

• East Asian mathematical journal
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• v.23 no.3
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• pp.313-326
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• 2007

The purpose of education of propositional logic is to understand the basic structure of the mathematics and to improve the logical thinking in normal life. But in the seventh curriculum, some basic terms, for examples $\wedge$ and $\vee$, are not introduced, the proposition $p{\\rightarrow}q$ is not defined properly, and use the wrong term $\Rightarrow$ so that it is difficult to understand the propositional logic. In this paper, we present a suitable content for the propositional logic in high-school mathematical class. We also present a proper definition of the proposition $p{x}{\Rightarrow}q{x}$ without using the notation $\rightarrow$. We finally give proper definitions of necessary conditions, sufficient conditions, and necessary and sufficient conditions.