The Experts below are selected from a list of 30 Experts worldwide ranked by ideXlab platform

Yuanhorng Lin - One of the best experts on this subject based on the ideXlab platform.

  • integration of fuzzy clustering and polytomous ordering theory to represent concepts of Equality Axiom for pupils
    International Journal of Kansei Information, 2011
    Co-Authors: Hekai Chen, Yuanhorng Lin
    Abstract:

    Representation of knowledge structure is the measurement related to human kansei engineering. Therefore, the purpose of this study is to provide an integrated method which could represent knowledge structure based on optimal clustering. Polytomous ordering theory is developed to represent knowledge structure and fuzzy clustering is to cluster students so that students of the same cluster have similar knowledge structure. An empirical data of mathematical Equality Axiom for pupils are discussed. Results show that the integrated methodology could represent knowledge structures effectively. This methodology will be help human kansei as to knowledge representation and useful for remedial instruction. Finally, some suggestions and recommendations for future research are discussed.

  • an integration of concept structure analysis and s p chart with application in Equality Axiom concepts diagnosis
    Intelligent Information Technology Application, 2008
    Co-Authors: Yuanhorng Lin, Jengming Yih
    Abstract:

    The purpose of this study is to discuss an integrated method which could provide diagnostic information for items and students. This integrated method combined two major methods. One is concept structure analysis and the other is student problem chart (S-P chart). The concept structure analysis could analyze individualized concepts structure and S-P chart could classify students and items into proper types so that diagnosis for remedial instruction is more feasible. The authors provide the empirical data analysis of Equality Axiom test. The results show that students with different learning types own varied concept structures. Finally, based on the findings and results, some suggestions and recommendations for future research are provided.

  • Fuzzy Application on Rule Space Approach and Graphic Knowledge Structure Representation for Equality Axiom Concepts
    2008 3rd International Conference on Innovative Computing Information and Control, 2008
    Co-Authors: Yuanhorng Lin, Hekai Chen, Shin-feng Chen
    Abstract:

    The purpose of this study is to provide an integrated methodology of fuzzy approach on rule space and graphic knowledge structure analysis. The authors adopt fuzzy c-means based on the information of latent trait and standardized caution index of students, which are from item response theory (IRT) and S-P chart respectively. This method is similar to the utility of rule space, which is provided Tatsuoka, but it is fuzzy clustering in this study. Another characteristic of this study is the graphic representation on knowledge structure by fuzzy structural modeling (FSM) and it is an individualized knowledge structure analysis. The clustering results and individualized knowledge structure analysis could provide important information for remedial instruction.

  • Concept structure analysis method based on integration of FLMP and ISM with application in Equality Axiom concepts
    2007
    Co-Authors: Yuanhorng Lin, Wen-liang Hung
    Abstract:

    The purpose of this study is to provide an integrated method which aims to analyze individualized concept structure. This method integrates algorithm of fuzzy logic model of perception (FLMP) and interpretive structural modeling (ISM). The combined algorithm of this integrated model could analyze the individualized concepts structure based on the comparisons with expert. The authors provide the empirical data analysis of Equality Axiom testing for pupils. The results show that task-takers with different response patterns and total score own varied concept structures. Finally, based on the findings and results, some suggestions and recommendations for future research are provided.

  • The Investigation of S-P Chart Analysis on the Test Evaluations of Equality Axiom Concepts for Sixth Graders
    2006
    Co-Authors: Yuanhorng Lin, Shau-ming Chen
    Abstract:

    The purpose of the study is to explore the feasibility of using S-P chart analysis on the item analysis for test of Equality Axiom. The S-P chart analysis could provide the two caution indices. One is the caution index for students (CS) and the other is the caution index for problems (CP). With these two indices, we could select items with proper qualities and understand the cognition and learning condition of students. The study shows that the usage of S-P chart analysis is a feasible and effective way for assessment analysis. Finally, based the findings of this study, some suggestions and recommendations are discussed.

Andy Galloway - One of the best experts on this subject based on the ideXlab platform.

  • Undefined Expressions and Logic in Z and B
    Formal Methods in System Design, 1999
    Co-Authors: Bill Stoddart, Steve Dunne, Andy Galloway
    Abstract:

    In this paper we show how undefined expressions and undetermined predicates may arise when using the specification languages Z and B. We review how undefined terms have been handled in various formalisms (Principia Mathematica, Domain Theory, LPF,) and look at the effect of undefined expressions on the proof theory and the denotational meaning of specifications in Z and B. We note that in formal systems which make use of partial functions and have an unguarded Equality Axiom x = x together with a classical two valued logic it is impossible to have a proof rules of the form y = f(x) ⇒ x ↦ y ∈ f and that consequently, assertions of the form y = f(x) may have very little meaning.

  • Undefined Expressions and Logic in Z and B
    Formal Methods in System Design, 1999
    Co-Authors: Bill Stoddart, Steve Dunne, Andy Galloway
    Abstract:

    In this paper we show how undefined expressions and undetermined predicates may arise when using the specification languages Z and B. We review how undefined terms have been handled in various formalisms (Principia Mathematica, Domain Theory, LPF,) and look at the effect of undefined expressions on the proof theory and the denotational meaning of specifications in Z and B. We note that in formal systems which make use of partial functions and have an unguarded Equality Axiom x e x together with a classical two valued logic it is impossible to have a proof rules of the form y e f(x) ⇒ x m y ∈ f and that consequently, assertions of the form y e f(x) may have very little meaning.

Masanao Ozawa - One of the best experts on this subject based on the ideXlab platform.

  • from boolean valued analysis to quantum set theory mathematical worldview of gaisi takeuti
    Mathematics, 2021
    Co-Authors: Masanao Ozawa
    Abstract:

    Gaisi Takeuti introduced Boolean valued analysis around 1974 to provide systematic applications of the Boolean valued models of set theory to analysis. Later, his methods were further developed by his followers, leading to solving several open problems in analysis and algebra. Using the methods of Boolean valued analysis, he further stepped forward to construct set theory that is based on quantum logic, as the first step to construct "quantum mathematics", a mathematics based on quantum logic. While it is known that the distributive law does not apply to quantum logic, and the Equality Axiom turns out not to hold in quantum set theory, he showed that the real numbers in quantum set theory are in one-to-one correspondence with the self-adjoint operators on a Hilbert space, or equivalently the physical quantities of the corresponding quantum system. As quantum logic is intrinsic and empirical, the results of the quantum set theory can be experimentally verified by quantum mechanics. In this paper, we analyze Takeuti’s mathematical world view underlying his program from two perspectives: set theoretical foundations of modern mathematics and extending the notion of sets to multi-valued logic. We outlook the present status of his program, and envisage the further development of the program, by which we would be able to take a huge step forward toward unraveling the mysteries of quantum mechanics that have persisted for many years.

  • from boolean valued analysis to quantum set theory mathematical worldview of gaisi takeuti
    arXiv: Quantum Physics, 2021
    Co-Authors: Masanao Ozawa
    Abstract:

    Gaisi Takeuti introduced Boolean valued analysis around 1974 to provide systematic applications of Boolean valued models of set theory to analysis. Later, his methods were further developed by his followers, leading to solving several open problems in analysis and algebra. Using the methods of Boolean valued analysis, he further stepped forward to construct set theory based on quantum logic, as the first step to construct "quantum mathematics", a mathematics based on quantum logic. While it is known that the distributive law does not apply to quantum logic, and the Equality Axiom turns out not to hold in quantum set theory, he showed that the real numbers in quantum set theory are in one-to-one correspondence with the self-adjoint operators on a Hilbert space, or equivalently the physical quantities of the corresponding quantum system. As quantum logic is intrinsic and empirical, the results of the quantum set theory can be experimentally verified by quantum mechanics. In this paper, we analyze Takeuti's mathematical world view underlying his program from two perspectives: set theoretical foundations of modern mathematics and extending the notion of sets to multi-valued logic. We outlook the present status of his program, and envisage the further development of the program, by which we would be able to take a huge step forward toward unraveling the mysteries of quantum mechanics that have persisted for many years.

Bill Stoddart - One of the best experts on this subject based on the ideXlab platform.

  • Undefined Expressions and Logic in Z and B
    Formal Methods in System Design, 1999
    Co-Authors: Bill Stoddart, Steve Dunne, Andy Galloway
    Abstract:

    In this paper we show how undefined expressions and undetermined predicates may arise when using the specification languages Z and B. We review how undefined terms have been handled in various formalisms (Principia Mathematica, Domain Theory, LPF,) and look at the effect of undefined expressions on the proof theory and the denotational meaning of specifications in Z and B. We note that in formal systems which make use of partial functions and have an unguarded Equality Axiom x = x together with a classical two valued logic it is impossible to have a proof rules of the form y = f(x) ⇒ x ↦ y ∈ f and that consequently, assertions of the form y = f(x) may have very little meaning.

  • Undefined Expressions and Logic in Z and B
    Formal Methods in System Design, 1999
    Co-Authors: Bill Stoddart, Steve Dunne, Andy Galloway
    Abstract:

    In this paper we show how undefined expressions and undetermined predicates may arise when using the specification languages Z and B. We review how undefined terms have been handled in various formalisms (Principia Mathematica, Domain Theory, LPF,) and look at the effect of undefined expressions on the proof theory and the denotational meaning of specifications in Z and B. We note that in formal systems which make use of partial functions and have an unguarded Equality Axiom x e x together with a classical two valued logic it is impossible to have a proof rules of the form y e f(x) ⇒ x m y ∈ f and that consequently, assertions of the form y e f(x) may have very little meaning.

Steve Dunne - One of the best experts on this subject based on the ideXlab platform.

  • Undefined Expressions and Logic in Z and B
    Formal Methods in System Design, 1999
    Co-Authors: Bill Stoddart, Steve Dunne, Andy Galloway
    Abstract:

    In this paper we show how undefined expressions and undetermined predicates may arise when using the specification languages Z and B. We review how undefined terms have been handled in various formalisms (Principia Mathematica, Domain Theory, LPF,) and look at the effect of undefined expressions on the proof theory and the denotational meaning of specifications in Z and B. We note that in formal systems which make use of partial functions and have an unguarded Equality Axiom x = x together with a classical two valued logic it is impossible to have a proof rules of the form y = f(x) ⇒ x ↦ y ∈ f and that consequently, assertions of the form y = f(x) may have very little meaning.

  • Undefined Expressions and Logic in Z and B
    Formal Methods in System Design, 1999
    Co-Authors: Bill Stoddart, Steve Dunne, Andy Galloway
    Abstract:

    In this paper we show how undefined expressions and undetermined predicates may arise when using the specification languages Z and B. We review how undefined terms have been handled in various formalisms (Principia Mathematica, Domain Theory, LPF,) and look at the effect of undefined expressions on the proof theory and the denotational meaning of specifications in Z and B. We note that in formal systems which make use of partial functions and have an unguarded Equality Axiom x e x together with a classical two valued logic it is impossible to have a proof rules of the form y e f(x) ⇒ x m y ∈ f and that consequently, assertions of the form y e f(x) may have very little meaning.