The theories of truth discussed thus far are all axiomatized in classical logic. Some authors have also looked into axiomatic theories of truth based on non-classical logic (see, for example, Field 2008, Halbach and Horsten 2006, Leigh and Rathjen 2012). There are a number of reasons why a logic weaker than classical logic may be preferred. The most obvious is that by weakening the logic, some collections of axioms of truth that were previously inconsistent become consistent. Another common reason is that the axiomatic theory in question intends to capture a particular non-classical semantics of truth, for which a classical background theory may prove unsound.