Semantic Derivation Verification

Automated Theorem Proving (ATP) systems are complex pieces of software, and thus may have bugs that make them unsound. In order to guard against such unsoundness, the derivations output by an ATP system may be semantically verified by a trusted system that checks the required semantic properties of each inference step. Such verification may need to be augmented by structural verification that checks that inferences have been used correctly in the context of the overall derivation. This paper describes techniques for semantic verification of derivations, and reports on their implementation in the DVDV verifier.

[1]  Andrei Voronkov,et al.  Splitting Without Backtracking , 2001, IJCAI.

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

[3]  Nuel D. Belnap,et al.  Entailment : the logic of relevance and necessity , 1975 .

[4]  Martin D. Davis,et al.  Obvious Logical Inferences , 1981, IJCAI.

[5]  Tanel Tammet,et al.  Towards Efficient Subsumption , 1998, CADE.

[6]  Lawrence Charles Paulson,et al.  Isabelle: A Generic Theorem Prover , 1994 .

[7]  William McCune,et al.  Mace4 Reference Manual and Guide , 2003, ArXiv.

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

[9]  Andrei Voronkov,et al.  The design and implementation of VAMPIRE , 2002, AI Commun..

[10]  Piotr Rudnicki.  Obvious inferences , 2004, Journal of Automated Reasoning.

[11]  William McCune,et al.  OTTER 3.3 Reference Manual , 2003, ArXiv.

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

[13]  Christoph Weidenbach,et al.  S PASS Version 2.0 , 2002, CADE.

[14]  Robert Veroff,et al.  Using hints to increase the effectiveness of an automated reasoning program: Case studies , 1996, Journal of Automated Reasoning.

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

[16]  K. Claessen,et al.  New Techniques that Improve MACE-style Finite Model Finding , 2007 .

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

[18]  Hans de Nivelle,et al.  Automated Proof Construction in Type Theory Using Resolution , 2000, Journal of Automated Reasoning.

[19]  Stephan Schulz,et al.  E - a brainiac theorem prover , 2002, AI Commun..

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

[21]  William McCune,et al.  Ivy: a preprocessor and proof checker for first-order logic , 2000 .

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