Graph-based Logic and Sketches Export

@article{citeulike:3311741, abstract = {We present the basic ideas of forms (a generalization of Ehresmann's sketches) and their theories and models, more explicitly than in previous expositions. Forms provide the ability to specify mathematical structures and data types in any appropriate category, including many types of structures (e.g. function spaces) that cannot be specified by sketches. We also outline a new kind of formal logic (based on graphs instead of strings of symbols) that gives an intrinsically categorial definition of assertion and proof for each type of form. This formal logic is new to this monograph. The relationship between multisorted equational logic and finite product theories is worked out in detail.}, archivePrefix = {arXiv}, author = {Bagchi, Atish and Wells, Charles}, citeulike-article-id = {3311741}, citeulike-linkout-0 = {http://arxiv.org/abs/0809.3023}, citeulike-linkout-1 = {http://arxiv.org/pdf/0809.3023}, day = {18}, eprint = {0809.3023}, keywords = {category-theory, math}, month = {Sep}, posted-at = {2009-08-03 08:00:55}, priority = {2}, title = {Graph-based Logic and Sketches}, url = {http://arxiv.org/abs/0809.3023}, year = {2008} }

TY - JOUR ID - citeulike:3311741 L3 - citeulike-article-id:3311741 N2 - We present the basic ideas of forms (a generalization of Ehresmann's sketches) and their theories and models, more explicitly than in previous expositions. Forms provide the ability to specify mathematical structures and data types in any appropriate category, including many types of structures (e.g. function spaces) that cannot be specified by sketches. We also outline a new kind of formal logic (based on graphs instead of strings of symbols) that gives an intrinsically categorial definition of assertion and proof for each type of form. This formal logic is new to this monograph. The relationship between multisorted equational logic and finite product theories is worked out in detail. TI - Graph-based Logic and Sketches KW - category-theory KW - math AU - Bagchi, Atish AU - Wells, Charles PY - 2008/Sep/18/ UR - http://arxiv.org/abs/0809.3023 ER -