The Balance Sheet and the Assets-Claims on Assets Relationship in the Axiomatic Method

The purpose of this study is to analyze the set structure of the balance sheet and assets-claims on assets relationship, considering the dual concept of monetary units, the axiomatic theory and accountingspecific axioms. The structure of the balance sheet and assets-claims on assets relationship are examined using a rationalistic, analytical and deductive method; this method uses the axiomatic set theory and predicate logic to define a set of axioms and the logical rationale to apply them to any deductive proof. The method includes accounting primitives and axioms to use in combination with those of the axiomatic theory. A direct proof is applied to test the balance sheet fit to a hereditary set structure according to the axiomatic theory, and proof by contraposition is employed to examine the assets-claims on assets equality by comparing their elements. Results show that balance sheet has a set structure that can be defined and analyzed with the axiomatic method and fits a hereditary set structure. Also, by comparing the elements of assets and claims on assets and considering their financial classification, it is shown that these sets do not contain the same elements and, consequently, they are not equal under the postulates of the axiomatic method. Key-Words: Dual concept, accounting transactions, axiomatic method, assets, claims on assets, balance sheet.