TPTP and Beyond: Representation of Quantified Non-Classical Logics

The practical employment of automated deduction systems requires the user to input problem statements in a well-formed string representation. While this presentation is usually fixed by the respective system, the various language dialects of the TPTP library are meanwhile accepted as a de-facto standard for all current automated theorem provers based on classical logics. In the context of reasoning in non-classical logics, however, only a few limited standardization approaches exist, with QMLTP being the most notable exception. To move standardization forward, we outline conservative extensions to the TPTP language that allow systematic syntax definitions for various expressive, non-classical logics. These logics include higher-order versions of modal logics, conditional logics, hybrid logics, free logics, and many-valued logics. We are convinced that a standard syntax for prominent non-classical logics will not only facilitate their deployment but also support the development and comparability of corresponding theorem proving systems.