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A formal approach to Gestalt theory

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A strange finding underlies this booklet. Looking for a formal expression of Gestalt theory the result was a relation between two completely different phenomena in cognition and perception research. Gestalt theory emphasizes that it is the observer who creates the experienced structures. The theory does not deny that there are structures outside. However, the human brain is not an information processing mechanism that projects the outside structures into the inside. It builds its own structures in sufficient harmony with its surroundings. For a researcher the interesting question is how this happens. An answer could give insight in how we learn language, how we interpret sound, how we perceive figures, and so on. There are rules and formal models that describe the outside conditions for inside experience, but these do not answer the question. This booklet is an attempt to give such an answer. Its result shows why these rules and formal models are successful in predicting experiences. But there is another result related to phenomena that at first sight has nothing to do with Gestalt theory. In cognitive psychology and language research one regularly notices that humans can process 5, 6 or 7 items in one event. In perception research one finds that subjects use two interpretations, one of which dominates. The first phenomenon is known as “seven minus two”, the second one as duality. In this study both phenomena appear to be strongly related. Combining the formal approach with the notion of associative memory leads to remarks on brain research, individual differences, and learning and forgetting.
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... In Section 1, we will briefly sketch the syntactic view on bound pronouns and we discuss the exceptional cases reported on by Leddon and Lidz [2]. After that, Section 2 introduces the key elements of Focus theory [3,4]. Section 3 is devoted to an application of the theory on the observed problematic cases, and, finally, Section 4 summarizes the main results of this paper. ...
... In the remainder of this paper, we would like to explore an alternative explanation for the difference between the two types of moved elements. In the next section, we will briefly introduce the Focus theory developed by Buffart [3]. ...
... The assumption that an element is involved in only one type of relation at the same time leads to a mathematical theorem (see in [3]) according to which each sequence with a length of maximal seven elements can be described by maximal two interpretations. In vision the existence of two interpretations is well known, It is called duality or complementarity. ...
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We propose an explanation of the observations of Leddon and Lidz that the predictions of binding theory are not always borne out by the facts. More specifically their participants did not always interpret bound pronouns in line with government and binding principles. Our analysis is based on a paper by Buffart and Jacobs where they recognized structures and substructures in languages in accordance with Focus theory. In the theory, every element in a structure, and thus an anaphor as well, is bound to it. In the absence of a reference within the main- or substructure, an anaphor may refer to an element in the related sub- or main structure. We show how preference works in case of duality of interpretations.
... It does not simply copy the input exactly as it appears. The booklet [1] gives a formal description of the theory and a mathematical proof that links the psychology theories of memory span [15][2] and duality [17]. Buffart states that: ...
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This paper describes a memory model with 3 levels of information. The lower-level stores source data, is Markov-like and unweighted. Then a middle-level ontology is created from a further 3 phases of aggregating source information, by transposing from an ensemble to a hierarchy at each level. The ontology is useful for search processes and the aggregating process transposes the information from horizontal set-based sequences to more vertical typed-based clusters. The base memory is essentially neutral, where any weighted constraints or preferences should be sent by the calling module. This therefore allows different weight sets to be imposed on the same linking structure. The success of the ontology typing is open to interpretation, but the author would suggest that when clustering text, the result was types based more on use and context, for example, 'linking' with 'structure' or 'provide' with 'web,' for a document describing distributed service-based networks. This allows the system to economise over symbol use, where links to related symbols will be clustered together. The author then conjectures that a third memory substrate would be more neural in nature and would include functions or operations to be performed on the data, along with related memory information.
Preprint
Full-text available
This paper describes a memory model with 2 levels of information. The lower-level stores source data, is Markov-like and unweighted. Then an upper-level ontology is created from a further 3 phases of aggregating source information, by transposing from an ensemble to a hierarchy at each level. The ontology is useful for search processes and the aggregating process transposes the information from horizontal set-based sequences to more vertical typed-based clusters. The base memory is essentially neutral, where any weighted constraints or preferences should be sent by the calling module. This therefore allows different weight sets to be imposed on the same linking structure. The success of the ontology typing is open to interpretation, but the author would suggest that when clustering text, the result was types based more on use and context, for example, 'linking' with 'structure' or 'provide' with 'web,' for a document describing distributed service-based networks. This allows the system to economise over symbol use, where links to related symbols will be clustered together. The author then conjectures that a third level would be more neural in nature and would include functions or operations to be performed on the data, along with related memory information.
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