A catalog of Boolean concepts Export

@article{citeulike:1670383, abstract = {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.}, author = {Feldman, Jacob}, citeulike-article-id = {1670383}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/S0022-2496(02)00025-1}, citeulike-linkout-1 = {http://www.sciencedirect.com/science/article/B6WK3-48JJJM1-9/2/c8d2cffdcc4bec41ffd9d026d898ddd2}, doi = {10.1016/S0022-2496(02)00025-1}, journal = {Journal of Mathematical Psychology}, keywords = {\_d\_informational-constraints, \_d\_methodological, category-learning-use, complexity}, month = {February}, number = {1}, pages = {75--89}, posted-at = {2007-09-18 21:35:40}, priority = {3}, title = {A catalog of Boolean concepts}, url = {http://dx.doi.org/10.1016/S0022-2496(02)00025-1}, volume = {47}, year = {2003} }

TY - JOUR ID - citeulike:1670383 L3 - citeulike-article-id:1670383 N2 - 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. IS - 1 JF - Journal of Mathematical Psychology EP - 89 TI - A catalog of Boolean concepts VL - 47 SP - 75 KW - _d_informational-constraints KW - _d_methodological KW - category-learning-use KW - complexity AU - Feldman, Jacob PY - 2003/02// UR - http://dx.doi.org/10.1016/S0022-2496(02)00025-1 ER -