Conflict Resolution: A First-Order Resolution Calculus with Decision Literals and Conflict-Driven Clause Learning

This paper defines the (first-order) conflict resolution calculus: an extension of the resolution calculus inspired by techniques used in modern Sat-solvers. The resolution inference rule is restricted to (first-order) unit propagation and the calculus is extended with a mechanism for assuming decision literals and with a new inference rule for clause learning, which is a first-order generalization of the propositional conflict-driven clause learning procedure. The calculus is sound (because it can be simulated by natural deduction) and refutationally complete (because it can simulate resolution), and these facts are proven in detail here.

[1]  L. Wos,et al.  Paramodulation and Theorem-Proving in First-Order Theories with Equality , 1983 .

[2]  Christoph Weidenbach,et al.  SPASS Version 3.5 , 2009, CADE.

[3]  Chad E. Brown,et al.  Satallax: An Automatic Higher-Order Prover , 2012, IJCAR.

[4]  Geoff Sutcliffe.  The TPTP Problem Library and Associated Infrastructure , 2009, Journal of Automated Reasoning.

[5]  Armin Biere,et al.  PicoSAT Essentials , 2008, J. Satisf. Boolean Model. Comput..

[6]  Peter Baumgartner,et al.  The Model Evolution Calculus , 2003, CADE.

[7]  Harald Ganzinger,et al.  Rewrite-Based Equational Theorem Proving with Selection and Simplification , 1994, J. Log. Comput..

[8]  Stephan Schulz,et al.  System Description: E 1.8 , 2013, LPAR.

[9]  Ross A. Overbeek,et al.  Complexity and related enhancements for automated theorem-proving programs , 1976 .

[10]  Konstantin Korovin,et al.  iProver - An Instantiation-Based Theorem Prover for First-Order Logic (System Description) , 2008, IJCAR.

[11]  G. Gentzen.  Untersuchungen über das logische Schließen. I , 1935 .

[12]  Peter Baumgartner,et al.  Lemma Learning in the Model Evolution Calculus , 2006, LPAR.

[13]  Peter Baumgartner,et al.  Model Evolution-Based Theorem Proving , 2014, IEEE Intelligent Systems.

[14]  Marijn J. H. Heule,et al.  DRAT-trim: Efficient Checking and Trimming Using Expressive Clausal Proofs , 2014, SAT.

[15]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[16]  Alan Robinson,et al.  Handbook of automated reasoning , 2001 .

[17]  Sharad Malik,et al.  Efficient conflict driven learning in a Boolean satisfiability solver , 2001, IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281).

[18]  Evert W. Beth,et al.  Semantic Entailment And Formal Derivability , 1955 .

[19]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[20]  Andrei Voronkov,et al.  AVATAR: The Architecture for First-Order Theorem Provers , 2014, CAV.

[21]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

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

[23]  Chad E. Brown.  Reducing Higher-Order Theorem Proving to a Sequence of SAT Problems , 2013, Journal of Automated Reasoning.

[24]  Joao Marques-Silva,et al.  GRASP-A new search algorithm for satisfiability , 1996, Proceedings of International Conference on Computer Aided Design.

[25]  Maria Paola Bonacina,et al.  On First-Order Model-Based Reasoning , 2015, Logic, Rewriting, and Concurrency.

[26]  Inês Lynce,et al.  Conflict-Driven Clause Learning SAT Solvers , 2009, Handbook of Satisfiability.

[27]  G. Gentzen.  Untersuchungen über das logische Schließen. II , 1935 .

[28]  Christoph Weidenbach,et al.  Combining Superposition, Sorts and Splitting , 2001, Handbook of Automated Reasoning.

[29]  Harald Ganzinger,et al.  Completion of First-Order Clauses with Equality by Strict Superposition (Extended Abstract) , 1990, CTRS.