First-order logic in 13th-century accounting systems

Ronald Fuller
Presented at the 2017 American Philosophical Association, Pacific Division conference, sessions for the Association for Symbolic Logic.

The system of interconnected books used in double-entry bookkeeping and other early accounting systems is precisely consistent with the relational model and, therefore, first-order logic. That means every object can be described in terms of the relational model and operated upon using a relational language. In other words, medieval merchants had created fully-functional, manually-operated relational database management systems, which exhibit quantification and relations with arities greater than one.

Primitive business institutions did not have the benefit of computers, but they enjoyed a particular advantage over their modern counterparts: a logic-literate merchant class. When the relational model was introduced in the 1970's it was falsely seen as a new computer-based method of organizing information, rather than a new computer-based way to automate old logic-based methods that had been used with success for nearly 700 years. Consequently, the responsibility to define logical vocabularies for information systems shifted to computer experts rather than business domain experts, leading to the widespread proliferation of defective ontologies that fail to meet organizational requirements. The de-emphasis of logic education since the 19th century is a significant factor in this predicament.