Empirically Successful Automated Reasoning in Large Theories

Decision procedures for checking satisfiability of logical formulas are crucial for many verification applications. Of particular recent interest are solvers for Satisfiability Modulo Theories (SMT). SMT solvers decide logical satisfiability (or dually, validity) of formulas in classical multi-sorted first-order logic with equality, with respect to a background theory. The success of SMT for verification applications is largely due to the suitability of supported background theories for expressing verification conditions. In this talk I will discuss how modern SMT solvers work, and the main implementation techniques used. I will also describe how SMT solvers are used in industry and Microsoft in particular.

[1]  Vasek Chvátal,et al.  A Greedy Heuristic for the Set-Covering Problem , 1979, Math. Oper. Res..

[2]  Michael R. Genesereth,et al.  Knowledge Interchange Format , 1991, KR.

[3]  U. Feige.  A threshold of ln n for approximating set cover , 1998, JACM.

[4]  W. Reif,et al.  Theorem Proving in Large Theories , 1998 .

[5]  Christoph Weidenbach,et al.  SPASS: Combining Superposition, Sorts and Splitting , 2000 .

[6]  Christiane Fellbaum,et al.  Book Reviews: WordNet: An Electronic Lexical Database , 1999, CL.

[7]  G. Sutcliffe.  The Design and Implementation of a Compositional Competition-Cooperation Parallel ATP System , 2001 .

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

[9]  Patrick J. Hayes,et al.  A Semantics for the Knowledge Interchange Format , 2001 .

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

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

[12]  Embarcadero Mountain,et al.  An English to Logic Translator for Ontology-based Knowledge Representation Languages , 2003 .

[13]  Adam Pease,et al.  Linking Lixicons and Ontologies: Mapping WordNet to the Suggested Upper Merged Ontology , 2003, IKE.

[14]  Koen Claessen,et al.  New techniques that improve mace-style model nding , 2003 .

[15]  Josef Urban.  MPTP – Motivation, Implementation, First Experiments , 2004, Journal of Automated Reasoning.

[16]  C. Tinelli,et al.  Darwin: A Theorem Prover for the Model Evolution Calculus , 2004 .

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

[18]  Monty Newborn,et al.  Octopus: Combining Learning and Parallel Search , 2004, Journal of Automated Reasoning.

[19]  Deepak Ramachandran,et al.  First-Orderized ResearchCyc : Expressivity and Efficiency in a Common-Sense Ontology , 2005 .

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

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

[22]  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.

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

[24]  Christiane Fellbaum,et al.  Building a WordNet for Arabic , 2006, LREC.

[25]  Lawrence C. Paulson,et al.  Lightweight relevance filtering for machine-generated resolution , 2006 .

[26]  Petr Pudlák.  Search for faster and shorter proofs using machine generated lemmas , 2006 .

[27]  Adam Pease,et al.  Linking FrameNet to the Suggested Upper Merged Ontology , 2006, FOIS.

[28]  Josef Urban,et al.  MizarMode - an integrated proof assistance tool for the Mizar way of formalizing mathematics , 2006, J. Appl. Log..

[29]  Geoff Sutcliffe,et al.  SRASS - A Semantic Relevance Axiom Selection System , 2007, CADE.

[30]  Lawrence C. Paulson,et al.  Lightweight relevance filtering for machine-generated resolution problems , 2009, J. Appl. Log..

[31]  Peter Baumgartner,et al.  Computing finite models by reduction to function-free clause logic , 2009, J. Appl. Log..