THF0 - The Core of the TPTP Language for Higher-Order Logic

One of the keys to the success of the Thousands of Problems for Theorem Provers (TPTP) problem library and related infrastructure is the consistent use of the TPTP language. This paper introduces the core of the TPTP language for higher-order logic --- THF0, based on Church's simple type theory. THF0 is a syntactically conservative extension of the untyped first-order TPTP language.

[1]  Per Martin-Löf,et al.  An intuitionistic theory of types , 1972 .

[2]  Natarajan Shankar,et al.  PVS: Combining Specification, Proof Checking, and Model Checking , 1996, FMCAD.

[3]  Jörg H. Siekmann,et al.  Computer supported mathematics with Omegamega , 2006, J. Appl. Log..

[4]  Volker Sorge,et al.  Proof Development with OMEGA , 2002, CADE.

[5]  Michael J. Witbrock,et al.  An Introduction to the Syntax and Content of Cyc , 2006, AAAI Spring Symposium: Formalizing and Compiling Background Knowledge and Its Applications to Knowledge Representation and Question Answering.

[6]  Christoph Benzmüller,et al.  System Description: LEO - A Higher-Order Theorem Prover , 1998, CADE.

[7]  Leon Henkin,et al.  Completeness in the theory of types , 1950, Journal of Symbolic Logic.

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

[9]  William C. Frederick,et al.  A Combinatory Logic , 1995 .

[10]  Giovanni Sambin,et al.  Twenty-five years of constructive type theory. , 1998 .

[11]  Adam Pease,et al.  Towards a standard upper ontology , 2001, FOIS.

[12]  Jaime G. Carbonell,et al.  Automated Deduction — CADE-16 , 2002, Lecture Notes in Computer Science.

[13]  William A. Howard,et al.  The formulae-as-types notion of construction , 1969 .

[14]  Furio Honsell,et al.  A framework for defining logics , 1993, JACM.

[15]  M. Gordon,et al.  Introduction to HOL: a theorem proving environment for higher order logic , 1993 .

[16]  Christoph Benzmüller,et al.  Progress Report on LEO-II -- An Automatic Theorem Prover for Higher-Order Logic , 2007 .

[17]  J. Roger Hindley,et al.  To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus, and Formalism , 1980 .

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

[19]  G. Frege.  Grundgesetze der Arithmetik , 1893 .

[20]  Piotr Rudnicki,et al.  An Overview of the MIZAR Project , 1992 .

[21]  Bernhard Schölkopf,et al.  A Tutorial Introduction , 2001 .

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

[23]  Koen Claessen,et al.  Using the TPTP Language for Writing Derivations and Finite Interpretations , 2006, IJCAR.

[24]  David Aspinall,et al.  Formalising Java's Data Race Free Guarantee , 2007, TPHOLs.

[25]  E. Zermelo.  Über Grenzzahlen und Mengenbereiche , 1930 .

[26]  Larry Wos,et al.  What Is Automated Reasoning? , 1987, J. Autom. Reason..

[27]  Christoph Benzmüller,et al.  A Structured Set of Higher-Order Problems , 2005, TPHOLs.

[28]  Alonzo Church,et al.  A formulation of the simple theory of types , 1940, Journal of Symbolic Logic.

[29]  Frank Pfenning,et al.  TPS: A theorem-proving system for classical type theory , 1996, Journal of Automated Reasoning.

[30]  Volker Sorge,et al.  Combined reasoning by automated cooperation , 2008, J. Appl. Log..

[31]  John Harrison,et al.  HOL Light: A Tutorial Introduction , 1996, FMCAD.

[32]  Geoff Sutcliffe,et al.  Extending the TPTP Language to Higher-Order Logic with Automated Parser Generation , 2006, IJCAR.

[33]  Weixiong Zhang,et al.  Distributed Constraint Problem Solving And Reasoning In Multi-Agent Systems , 2004 .

[34]  Patrice Godefroid,et al.  Software Model Checking: The VeriSoft Approach , 2005, Formal Methods Syst. Des..

[35]  Geoff Sutcliffe,et al.  TPTP, TSTP, CASC, etc , 2007, CSR.

[36]  Geoff Sutcliffe,et al.  The TPTP Problem Library , 1994, Journal of Automated Reasoning.

[37]  R. Petit.  A Tutorial Introduction , 1980 .

[38]  Ian Green,et al.  System Description: Proof Planning in Higher-Order Logic with Lambda-Clam , 1998, CADE.

[39]  Frank Pfenning,et al.  System Description: Twelf - A Meta-Logical Framework for Deductive Systems , 1999, CADE.

[40]  Geoff Sutcliffe,et al.  TSTP Data-Exchange Formats for Automated Theorem Proving Tools , 2004 .

[41]  Christoph Benzmüller,et al.  Higher-order semantics and extensionality , 2004, Journal of Symbolic Logic.

[42]  Michael Beeson,et al.  OTTER-LAMBDA, A THEOREM-PROVER WITH UNTYPED LAMBDA-UNIFICATION , 2004 .

[43]  Tobias Nipkow,et al.  A Proof Assistant for Higher-Order Logic , 2002 .