COMBINING MIZAR AND TPTP SEMANTIC PRESENTATION AND VERIFICATION TOOLS

This paper describes a combination of several Mizar-based tools (the MPTP translator, XSL style sheets for Mizar), and TPTP-based tools (IDV, AGInT, SystemOnTPTP, GDV) used for visualizing, analyzing, and independent verication of Mizar proofs. The combination delivers to the readers of the Mizar Mathematical Library (MML) an easy, powerful, and almost playful way of exploring the semantics and the structure of the li- brary. The key factors for the relative easiness of having these functionalities are the choice of XML as both internal and external interface of Mizar, and the existence of a TPTP representation of MML articles. This shows the great added value that can be obtained by cooperation of several quite di- verse (and quite often separately developed) projects, provided that they are based on the same communication standards.

[1]  Josef Urban,et al.  Momm - Fast Interreduction and Retrieval in Large Libraries of Formalized Mathematics , 2006, Int. J. Artif. Intell. Tools.

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

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

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

[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]  Geoff Sutcliffe,et al.  An Interactive Derivation Viewer , 2007, UITP@FLoC.

[7]  Josef Urban,et al.  ATP Cross-Verification of the Mizar MPTP Challenge Problems , 2007, LPAR.

[8]  Yi Gao,et al.  Automated Generation of Interesting Theorems , 2006, FLAIRS.

[9]  Josef Urban,et al.  XML-izing Mizar: Making Semantic Processing and Presentation of MML Easy , 2005, MKM.

[10]  Stephan Schulz A Comparison of Different Techniques for Grounding Near-Propositional CNF Formulae , 2002, FLAIRS Conference.

[11]  Yatsuka Nakamura,et al.  The Fashoda Meet Theorem for Rectangles , 2005 .

[12]  Josef Urban,et al.  MPTP 0.2: Design, Implementation, and Initial Experiments , 2006, Journal of Automated Reasoning.

[13]  Josef Urban,et al.  MaLARea SG1- Machine Learner for Automated Reasoning with Semantic Guidance , 2008, IJCAR.

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

[15]  Lawrence C. Paulson,et al.  Translating higher-order problems to first-order clauses , 2006 .

[16]  Serge Autexier,et al.  The MathServe System for Semantic Web Reasoning Services , 2006, IJCAR.

[17]  Geoff Sutcliffe,et al.  Semantic Derivation Verification , 2005, FLAIRS Conference.

[18]  Simon Colton,et al.  Automatic Construction and Verification of Isotopy Invariants , 2006, IJCAR.