Data processing: artificial intelligence – Knowledge processing system
Reexamination Certificate
1998-11-16
2001-10-09
Davis, George B. (Department: 2122)
Data processing: artificial intelligence
Knowledge processing system
C706S050000, C434S322000, C705S007380, C707S793000
Reexamination Certificate
active
06301571
ABSTRACT:
BACKGROUND OF THE INVENTION
This invention relates generally to methods and systems for testing humans and systems and the subsequent classification of humans into knowledge states and systems (including human systems) into functionality states. More specifically, the invention relates to computer-implemented testing and classification systems.
The process of testing and classification requires meaningful and accurate representations of the subject domains in terms of domain states. A domain state that a test subject is in is determined by sequentially administering to the test subject test items involving different aspects of the subject domain. The responses of the test subject to the test items determines the state of the test subject in the subject domain.
The implementation of such a testing and classification process by means of a computer has the potential of providing an efficient and effective means for identifying the remedial actions required to bring the test subject to a higher level of knowledge or functionality.
The partially ordered set (“poset”) is a natural model for the cognitive and functionality domains. Two states i and j in a poset model S may be related to each other in the following manner. If a test subject in state i can respond positively to all the test items to which a test subject in state j can, but a test subject in state j may not be able to respond positively to all the test items to which a test subject in state i can, we say that i contains j and denote this by the expression i≧j. Note that a positive response on any item should provide at least as much evidence for the test subject being in state i as in state j. Thus, the domain states are partially ordered by the binary “i contains j” relation. Note that the cognitive level or the functionality level of a test subject in state i is equal to or higher than that of a test subject in state j. Similarly, the cognitive level or the functionality level of a test subject in state j is equal to or lower than that of a test subject in state i. Accordingly, state i is said to be equal to or higher than state j and state j is said to be equal to or lower than state i.
Poset models in an educational context have been proposed before. However, they have either been Boolean lattices or posets closed under union in the sense that the union of any two members of the poset is also in the poset. This restriction is undesirable in that it leads to models that can be quite large. For example, allowing the number of test items to define the model can lead to models with as many as 2
N
possible states where N is equal to the number of test items. With this approach the responses to the test items permits immediate classification with very little analysis. However, having such overly large models ultimately results in poor classification performance.
When sequential item selection rules have been used in classifying states in a poset, the approach has not been accomplished in a decision-theoretic context. Consequently, there was no assurance that the classification process would converge rapidly nor, in fact, that it would converge at all.
There is a need for a testing and classification system which is based on sound scientific and mathematical principles and which, as a result, can accurately and efficiently determine the domain states of humans and systems. It is reasonable to base such a system on poset models, but it should be possible to use general, even non-finite posets rather than the specialized posets that are typical of present-day systems. It is important that model selection and fitting for any particular domain be based on appropriate analysis rather than simply a result of the choice of test items. Similarly, the selection of test items should be based on appropriate analysis with reference to the domain model rather than being a more-or-less ad hoc process that ultimately gives birth to its own domain model.
BRIEF SUMMARY OF THE INVENTION
The invention is a method for interacting with a test subject with respect to knowledge or functionality characterized by a plurality of states in one or more domains. A domain is a set of facts, a set of values, or a combination of a set of facts and a set of values. The set of facts for a knowledge domain is any set of facts. The set of facts for a functionality domain is a set of facts relating to the functionality of a test subject. A state is denoted as a fact state, a value state, or a combination state, a fact state being characterized by a subset of facts, a value state being characterized by a subset of values, and a combination state being characterized by a combination of a subset of facts and a subset of values.
A first state is higher than or equal to a second state and a second state is lower than or equal to a first state if (1) the subset of facts or a subset of values associated with the first state respectively includes the subset of facts or is greater than or equal to the subset of values associated with the second state or (2) the subset of facts and the subset of values associated with the first state respectively includes the subset of facts and is greater than or equal to the subset of values associated with the second state.
The method comprises steps (a),(b),(c),(d),(e), and (z). Step (a) consists of specifying one or more domains where each domain comprises a plurality of states and determining the higher-lower-neither relationships for each state in each domain, the higher-lower-neither relationships for a state being a specification of which states are higher, which states are lower, and which states are neither higher or lower.
Step (b) consists of specifying a domain pool for each domain comprising a plurality of test item blocks. A test item block consists of one or more test items where a test item administered to a test subject results in one of a plurality of possible responses.
Step (c) consists of specifying a class conditional density f
ibd
(x|s) for each test item i in test item block b for domain d for each state s in each domain. A class conditional density is a specification of the probability of a test subject in state s of domain d providing a response x to the test item i in the test item block b. Each test item partitions one or more domains into a plurality of partitions according to the class conditional densities associated with the test item. A partition is a subset of states for which the class conditional densities are the same or the union of such subsets.
Step (d) consists of selecting one or more test item blocks from the one or more domain pools to be administered to a test subject, and step (e) consists of processing the responses of the test subject to the one or more test item blocks administered to the test subject. The relationship of the test subject to domains is representable by a state probability set (SPS).
Step (z) consists of repeating the method from step (d) until method termination criteria are satisfied.
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Davis George B.
Malm Robert E.
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