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An Infrastructure for Typed Higher-order Form Automated Theorem Proving


There is a well established infrastructure that supports research and development 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. Research and development of ATP for higher-order logic has been in progress for as long as that for first-order logic. However, the computational issues that must be faced are significantly harder than those in first-order ATP, and the state of the art in higher-order ATP is not as advanced as that of first-order ATP. While there are several effective interactive systems for reasoning in higher-order logic, there is limited automation. Critically, research and development has not been supported by a commonly accepted infrastructure that provides leverage for progress leading to effective and successful application. This proposed research will develop an infrastructure, corresponding to that in place for first-order ATP, for higher-order ATP in Church's simple type theory. The effect will be to support research, development, and deployment of higher-order ATP systems, so that they can be used as effective components of academic and industrial processes. The long-term goal, beyond this proposed research, is to provide an infrastructure that extends to other forms of higher-order logic that extend Church's simple type theory, e.g. intiutionistic type theory.

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66123 Saarbrucken
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 130 109,59
Administrative Contact
Corinna Hahn