Semantic rules link purely theoretical terms like “price” and “electron” to things we can measure. Without them, theories cannot be tested empirically. When inappropriate, they produce false rejections. Economists routinely ignore semantic rules. Empirical journal articles essentially never mention them. More to the point, the conventional tests that reject the Law of One Price and Purchasing Power Parity never consider them. As a result, those rejections are unwarranted because such tests use inappropriate semantic rules. Both theories should be restored to not rejected and then retested using the more appropriate semantic rules described here. By using appropriate semantic rules, this paper is able to combine Covered Interest Parity and Purchasing Power Parity into a single theory that links auction markets for financial assets and commodities to auction markets for exchange rates. Using appropriate semantic rules for both theories also explains several puzzles in open economy macroeconomics and opens up broad new vistas for research.