The THFTPTP Project --- An Infrastructure for Typed Higher-order Form Automated Theorem Proving Marie Curie International Incoming Fellowship Grant Agreement PIIF-GA-2008-219982 Project Report --- Implications

There is a well established infrastructure that supports research, development, and deployment of firstorder 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. 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 has been 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. The completed THFTPTP project has developed an infrastructure that supports research and development of automated theorem proving in higher-order logic. The effect of the completed research 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.

[1]  Christoph Benzmüller.  Automating Access Control Logics in Simple Type Theory with LEO-II (Techreport) , 2009, SEC.

[2]  Christoph Benzmüller,et al.  Automating Quantified Multimodal Logics in Simple Type Theory -- A Case Study , 2009, ArXiv.

[3]  Geoff Sutcliffe.  The SZS Ontologies for Automated Reasoning Software , 2008, LPAR Workshops.

[4]  van Ls Bert Benthem Jutting,et al.  Checking Landau's “Grundlagen” in the Automath System: Appendices 3 and 4 (The PN-lines; Excerpt for “Satz 27”) , 1994 .

[5]  E. Landau,et al.  Grundlagen der Analysis , 1934 .

[6]  Chad E. Brown.  M-Set Models , 2007 .

[7]  Deepak Garg.  Principal-Centric Reasoning in Constructive Authorization Logic , 2009 .

[8]  Lawrence C. Paulson,et al.  Exploring Properties of Normal Multimodal Logics in Simple Type Theory with LEO-II , 2008 .

[9]  Geoff Sutcliffe,et al.  Progress in the Development of Automated Theorem Proving for Higher-Order Logic , 2009, CADE.

[10]  Chad Edward Brown,et al.  Dependently Typed Set Theory , 2006 .

[11]  Lawrence C. Paulson,et al.  Multimodal and intuitionistic logics in simple type theory , 2010, Log. J. IGPL.

[12]  Christoph Kreitz,et al.  The ILTP Problem Library for Intuitionistic Logic , 2007, Journal of Automated Reasoning.

[13]  Lawrence C. Paulson,et al.  LEO-II - A Cooperative Automatic Theorem Prover for Classical Higher-Order Logic (System Description) , 2008, IJCAR.

[14]  Geoff Sutcliffe,et al.  Evaluation of Systems for Higher-order Logic (ESHOL) , 2008, PAAR/ESHOL.

[15]  Martín Abadi,et al.  A Modal Deconstruction of Access Control Logics , 2008, FoSSaCS.

[16]  Geoff Sutcliffe,et al.  THF0 - The Core of the TPTP Language for Higher-Order Logic , 2008, IJCAR.

[17]  Geoff Sutcliffe,et al.  The state of CASC , 2006, AI Commun..