International Encyclopedia of the Social & Behavioral Sciences, 2001
This article describes some Markovian procedures designed for assessing the competence of individ... more This article describes some Markovian procedures designed for assessing the competence of individuals, such as school children, regarding a particular topic. The Markovian search takes place in a ‘knowledge structure,’ a combinatoric object gathering all the feasible ‘knowledge states.’ Each knowledge state is a subset of questions that could be mastered by some individual. Two Markovian classes of procedures are outlined in this article. In the most important one, each state of a Markov process is a probability distribution on the knowledge structure.
The automated real-time instructional system (ARIS) is a small computer-assisted instructional sy... more The automated real-time instructional system (ARIS) is a small computer-assisted instructional system written to run under the UNIX operating system on a PDP-11/34A machine. ARIS is a tool used to provide highly individualized instruction and, at the same time, to study the process of learning by keeping detailed records of students' actions. Currently, the system is used to teach logic and set theory. This paper describes the general philosophy, operation, and implementation of ARIS.
We establish a necessary and sufficient condition for a function defined on a subset of an algebr... more We establish a necessary and sufficient condition for a function defined on a subset of an algebra of sets to be extendable to a positive additive function on the algebra. It is also shown that this condition is necessary and sufficient for a regular function defined on a regular subset of the Borel algebra of subsets of a given compact Hausdorff space to be extendable to a measure.
The accuracy of the Content should not be relied upon and should be independently verified with p... more The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden.
This paper presents a theory describing the emergence and the evolution of preference relations o... more This paper presents a theory describing the emergence and the evolution of preference relations over (real) time. The subject or consumer is regarded as immersed in a random environment of the Poisson type. Events arise at random times, which consist of tokens of information about the alternatives. Some of these tokens have the potential to create or modify some edges
This sequence can be coded as a "word" xjf..z and a complete set of such words forms a "descripti... more This sequence can be coded as a "word" xjf..z and a complete set of such words forms a "descriptive language" for the family $. This class of languages is defined precisely, and some connections between such languages and families of sets are investigated. It is shown in particular that when + is closed under intersections and unions, and satisfies the topological condition known as T,, then I) can be recovered exactly from any of its descriptive languages. These results have an application in the assessment of knowledge. In this framework, the set X is a set of questions, and any set SE I) represents a possible knowledge state, containing all the questions that some individual is capable of solving. A subclass of the descriptive languages are then the "assessment languages." Any such language defines a nonredundant algorithm for determining the knowledge state of any individual.
This paper presents the axioms of a real time random walk on the set of states of a medium and so... more This paper presents the axioms of a real time random walk on the set of states of a medium and some of their consequences, such as the asymptotic probabilities of the states. The states of the random walk coincide with those of the medium, and the transitions of the random walk are governed by a probability distribution on the set of token-events, together with a Poisson process regulating the arrivals of such events. We examine two special cases. The first is the medium on strict weak orders on a set of three elements, the second the medium of strict partial orders on the same set. Thus, in each of these cases, a state of the medium is a binary relation. We also consider tune in-and-out extensions of these two special cases. We review applications of these models to opinion poll data pertaining to the 1992 United States presidential election. Each strict weak order or strict partial order is interpreted as being the implicit or explicit opinion of some individual regarding the three major candidates in that election, namely, Bush, Clinton and Perot. In particular, the strict partial order applications illustrate our notion of a response function that provides the link between theory and data in situations where, in contrast to previous papers, the permissible responses do not span the entire set of permissible states of the medium.
... Visual representation enhances learning. ... See Johnson-Laird & Byrne (1991) for... more ... Visual representation enhances learning. ... See Johnson-Laird & Byrne (1991) for more on this use of mental models. ... early reн searchers in choice and decision-making, who recognized the need for apн proximations and simplifications to decision-theoretic formulations (Simon ...
PART I: BACKGROUND 1. Ordinal Measurement 2. Extensive Measurement 3. Functional Equations PART I... more PART I: BACKGROUND 1. Ordinal Measurement 2. Extensive Measurement 3. Functional Equations PART II: THEORY 4. Fechner's Problem 5. Models of Discrimination 6. Psychometric Functions 7. Further Topics on Psychometric Functions 8. Weber Functions - Weber's Law 9. Psychophysical Methods 10. Signal Detection Theory 11. Psychophysics with Several Variables or Channels 12. Homogenity Laws 13. Scaling 14. Meaningful Psychophysical Laws
International Encyclopedia of the Social & Behavioral Sciences, 2001
This article describes some Markovian procedures designed for assessing the competence of individ... more This article describes some Markovian procedures designed for assessing the competence of individuals, such as school children, regarding a particular topic. The Markovian search takes place in a ‘knowledge structure,’ a combinatoric object gathering all the feasible ‘knowledge states.’ Each knowledge state is a subset of questions that could be mastered by some individual. Two Markovian classes of procedures are outlined in this article. In the most important one, each state of a Markov process is a probability distribution on the knowledge structure.
The automated real-time instructional system (ARIS) is a small computer-assisted instructional sy... more The automated real-time instructional system (ARIS) is a small computer-assisted instructional system written to run under the UNIX operating system on a PDP-11/34A machine. ARIS is a tool used to provide highly individualized instruction and, at the same time, to study the process of learning by keeping detailed records of students' actions. Currently, the system is used to teach logic and set theory. This paper describes the general philosophy, operation, and implementation of ARIS.
We establish a necessary and sufficient condition for a function defined on a subset of an algebr... more We establish a necessary and sufficient condition for a function defined on a subset of an algebra of sets to be extendable to a positive additive function on the algebra. It is also shown that this condition is necessary and sufficient for a regular function defined on a regular subset of the Borel algebra of subsets of a given compact Hausdorff space to be extendable to a measure.
The accuracy of the Content should not be relied upon and should be independently verified with p... more The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden.
This paper presents a theory describing the emergence and the evolution of preference relations o... more This paper presents a theory describing the emergence and the evolution of preference relations over (real) time. The subject or consumer is regarded as immersed in a random environment of the Poisson type. Events arise at random times, which consist of tokens of information about the alternatives. Some of these tokens have the potential to create or modify some edges
This sequence can be coded as a "word" xjf..z and a complete set of such words forms a "descripti... more This sequence can be coded as a "word" xjf..z and a complete set of such words forms a "descriptive language" for the family $. This class of languages is defined precisely, and some connections between such languages and families of sets are investigated. It is shown in particular that when + is closed under intersections and unions, and satisfies the topological condition known as T,, then I) can be recovered exactly from any of its descriptive languages. These results have an application in the assessment of knowledge. In this framework, the set X is a set of questions, and any set SE I) represents a possible knowledge state, containing all the questions that some individual is capable of solving. A subclass of the descriptive languages are then the "assessment languages." Any such language defines a nonredundant algorithm for determining the knowledge state of any individual.
This paper presents the axioms of a real time random walk on the set of states of a medium and so... more This paper presents the axioms of a real time random walk on the set of states of a medium and some of their consequences, such as the asymptotic probabilities of the states. The states of the random walk coincide with those of the medium, and the transitions of the random walk are governed by a probability distribution on the set of token-events, together with a Poisson process regulating the arrivals of such events. We examine two special cases. The first is the medium on strict weak orders on a set of three elements, the second the medium of strict partial orders on the same set. Thus, in each of these cases, a state of the medium is a binary relation. We also consider tune in-and-out extensions of these two special cases. We review applications of these models to opinion poll data pertaining to the 1992 United States presidential election. Each strict weak order or strict partial order is interpreted as being the implicit or explicit opinion of some individual regarding the three major candidates in that election, namely, Bush, Clinton and Perot. In particular, the strict partial order applications illustrate our notion of a response function that provides the link between theory and data in situations where, in contrast to previous papers, the permissible responses do not span the entire set of permissible states of the medium.
... Visual representation enhances learning. ... See Johnson-Laird & Byrne (1991) for... more ... Visual representation enhances learning. ... See Johnson-Laird & Byrne (1991) for more on this use of mental models. ... early reн searchers in choice and decision-making, who recognized the need for apн proximations and simplifications to decision-theoretic formulations (Simon ...
PART I: BACKGROUND 1. Ordinal Measurement 2. Extensive Measurement 3. Functional Equations PART I... more PART I: BACKGROUND 1. Ordinal Measurement 2. Extensive Measurement 3. Functional Equations PART II: THEORY 4. Fechner's Problem 5. Models of Discrimination 6. Psychometric Functions 7. Further Topics on Psychometric Functions 8. Weber Functions - Weber's Law 9. Psychophysical Methods 10. Signal Detection Theory 11. Psychophysics with Several Variables or Channels 12. Homogenity Laws 13. Scaling 14. Meaningful Psychophysical Laws
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