CORDIS - EU research results

An Infrastructure for Typed Higher-order Form Automated Theorem Proving

Final Report Summary - THFTPTP (An infrastructure for typed higher-order form automated theorem proving)

There is a well established infrastructure that supports research, development, and deployment of first-order Automated Theorem Proving (ATP) systems, stemming from the Thousands of Problems for Theorem Provers (TPTP) problem library. This infrastructure includes the TPTP itself, the TPTP language and SZS result ontology, the Thousands of Solutions from Theorem Provers (TSTP) solution library, various tools associated with the libraries, and the CADE ATP System Competition (CASC). This infrastructure has been central to the impressive progress that has been made in the development of high performance first-order ATP systems.

Summary of accomplishments

The completed THFTPTP project has developed an infrastructure that supports research and development of automated theorem proving in classical higher-order logic. The software components designed and developed are:
- A higher-order TPTP language to express problems and solutions in higher-order logic.
- A collection of higher-order test problems in the TPTP.
- A result and output ontology for higher-order ATP, extending the existing SZS ontology.
- A collection of higher-order problem solutions in the TSTP.
- Tools for preparing, processing, and analysing higher-order ATP problems and solutions.

The completed project has been the topic of, or has contributed to, paper publications, grant proposals, presentations, and events:
- Two conference papers directly about the project, plus two recent journal papers.
- Two workshop papers about the project and supporting topics.
- Five other papers describing work in which the new TPTP THF infrastructure was tested and employed.
- Three grant proposals that were strongly influenced by the project.
- Seven presentations related to the project.
- Six conferences at which either the host or researcher promoted use of the TPTP and the THF format.
- The new THF division of the CADE ATP System Competition (CASC)

The completed project has had significant impact:
- Effective support for the development of new and more powerful ATP systems for higher-order logic, and their application to a range of existing and new application domains.
- Seeding of multiple new research directions and projects: projects that will develop new principles and practice of automated theorem proving for higher-order logic, the use of higher-order logic for theorem proving in non-classical logics, and further development of the TPTP THF infrastructure.
- Quantifiable transfer of knowledge and expertise to Europe: to the host, researchers and students at the host university, and to eleven further institutions in Europe. Further unquantified development of expertise and knowledge follows from the interaction of the host and researcher with colleagues in Europe and beyond.


The THFTPTP project has delivered all the software products described in the project proposal, and additionally the project has contributed to the development of five fully automated ATP systems for higher-order logic in the THF format.

Implications and future research

The combined first-order and higher-order TPTP infrastructure now supports experimentation with different logic encodings. For example, it supports the comparison of provers for first-order and higher-order logics for the same abstract problems but different logic level formalisations. Collaborative links have been established with Jens Otten's new project at Potsdam University, which aims to build a problem library for multi-modal logics. A future goal is to also facilitate comparison between special purpose provers for quantified multi-modal logics and our higher-order theorem provers.

Future work includes the development and implementation of a powerful representation, verification, and explanation framework for THF proofs.