A dynamical approach to logical decisions

The ability of the human brain to carry out logical reasoning can be interpreted, in general, as a by-product of adaptive capacities of complex neural networks. Thus, we seek to base abstract logical operations in the general properties of neural networks designed as learning modules. We show that logical operations executable by McCulloch-Pitts binary networks can also be programmed in analog neural networks built with associative memory modules that process inputs as logical gates. These modules can interact among themselves to generate dynamical systems that extend the repertoire of logical operations. We demonstrate how the operations of the exclusive-OR or the implication appear as outputs of these interacting modules. In particular, we provide a model of the exclusive-OR that succeeds in evaluating an odd number of options (the exclusive-OR of classical logic fails in his case), thus paving the way for a more reasonable biological model of this important logical operator. We propose that a brain trained to compute can associate a complex logical operation to an orderly structured but temporary contingent episode by establishing a codified association among memory modules. This explanation offers an interpretation of complex logical processes (eventually learned) as associations of contingent events in memorized episodes. We suggest, as an example, a cognitive model that describes these "logical episodes".

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Dynamic searching in the brain

Mizraji

Valle-Lisboa

2009

Cogn Neurodyn

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Cognitive functions rely on the extensive use of information stored in the brain, and the searching for the relevant information for solving some problem is a very complex task. Human cognition largely uses biological search engines, and we assume that to study cognitive function we need to understand the way these brain search engines work. The approach we favor is to study multimodular network models, able to solve particular problems that involve searching for information. The building blocks of these multimodular networks are the context dependent memory models we have been using for almost 20 years. These models work by associating an output to the Kronecker product of an input and a context. Input, context and output are vectors that represent cognitive variables. Our models constitute a natural extension of the traditional linear associator. We show that coding the information in vectors that are processed through association matrices, allows for a direct contact between these memory models and some procedures that are now classical in the Information Retrieval field. One essential feature of context-dependent models is that they are based on the thematic packing of information, whereby each context points to a particular set of related concepts. The thematic packing can be extended to multimodular networks involving input-output contexts, in order to accomplish more complex tasks. Contexts act as passwords that elicit the appropriate memory to deal with a query. We also show toy versions of several 'neuromimetic' devices that solve cognitive tasks as diverse as decision making or word sense disambiguation. The functioning of these multimodular networks can be described as dynamical systems at the level of cognitive variables.

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A dynamical approach to logical decisions

Cited by 8 publications

References 15 publications

Password Authentication Using Context-Sensitive Associative Memory Neural Networks: A Novel Approach

Password Authentication Using Context-Sensitive Associative Memory Neural Networks: A Novel Approach

Logic in a Dynamic Brain

Dynamic searching in the brain

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