The Accounting Properties of Economic Events (Part II: Formalization)

The accounting theory formulated in Part I of this study posits that a set of accounting transactions is syntactically consistent and semantically complete if and only if it respects three accounting properties of economic events: independence, structural coupling, and compositionality. This theory is formalized mathematically in this paper (Part II). With the help of graph theory and computational linguistics, the journal of accounting transactions is modeled as an acyclic flow network and the accounting database is organized as a Cartesian-product diagram (recording processes). With the help of algebraic tools, the processing of accounting information is organized into three complementary reporting spaces: incidence, topological, and affine (reporting processes). The cornerstone of this formalization is a seemingly trivial fact: expenditures, expenses, revenues, and cash flows are modeled as darts of the accounting networks, in contrast to current practice that models expenses and revenues as vertices.