Mental models: towards a cognitive science of language, inference, and consciousness
Mental models: towards a cognitive science of language, inference, and consciousness
The complexity of Boolean functions
The complexity of Boolean functions
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
On the Length of Programs for Computing Finite Binary Sequences
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Embodiments of Mind
Proceedings of the 5th symposium on Applied perception in graphics and visualization
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Boolean concepts are concepts whose membership is determined by a Boolean function, such as that expressed by a formula of propositional logic. Certain Boolean concepts have been much studied in the psychological literature, in particular with regard to their ease of learning. But research attention has been somewhat uneven, with a great deal of attention paid to certain concepts and little to others, in part because of the unavailability of a comprehensive catalog. This paper gives a complete classification of Boolean concepts up to congruence (isomorphism of logical form). Tables give complete details of all concepts determined by up to four Boolean variables. For each concept type, the tables give a canonic logical expression, an approximately minimal logical expression, the Boolean complexity (length of the minimal expression), the number of distinct Boolean concepts of that type, and a pictorial depiction of the concept as a set of vertices in Boolean D-space. Some psychological properties of Boolean concepts are also discussed.