Graph-based Logic and Sketches

Details Graph-based Logic and Sketches Graph-based Logic and Sketches

2008-09-18

arxiv.org/abs/0809.3023v1

Mathematics

Category Theory

PDFLaTeX with xy-pic. 112 pages, 182 diagrams

Scientific paper

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.

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