On Unit-Refutation Complete Formulae with Existentially Quantified Variables

We analyze, along the lines of the knowledge compilation map, both the tractability and the succinctness of the propositional language URC-C of unit-refutation complete propositional formulae, as well as its disjunctive closure URC-C[V, ∃], and a superset of URC-C where variables can be existentially quantified and unit-refutation completeness concerns only consequences built up from free variables.

[1]  Pierre Marquis.  Existential Closures for Knowledge Compilation , 2011, IJCAI.

[2]  Pierre Marquis,et al.  Extending the Knowledge Compilation Map: Closure Principles , 2008, ECAI.

[3]  Pierre Marquis,et al.  A Knowledge Compilation Map , 2002, J. Artif. Intell. Res..

[4]  Alvaro del Val.  Tractable Databases: How to Make Propositional Unit Resolution Complete Through Compilation , 1994, KR.

[5]  Toby Walsh,et al.  Encodings of the Sequence Constraint , 2007, CP.

[6]  Toby Walsh,et al.  Local Consistencies in SAT , 2003, SAT.

[7]  Jean Christoph Jung,et al.  Two Encodings of DNNF Theories , 2008 .

[8]  Dan Roth,et al.  On the Hardness of Approximate Reasoning , 1993, IJCAI.

[9]  Joao Marques-Silva,et al.  Knowledge Compilation with Empowerment , 2012, SOFSEM.

[10]  Johannes Klaus Fichte,et al.  Clause-Learning Algorithms with Many Restarts and Bounded-Width Resolution , 2011, J. Artif. Intell. Res..

[11]  Carsten Sinz.  Knowledge Compilation for Product Configuration , 2002 .

[12]  Fahiem Bacchus,et al.  GAC Via Unit Propagation , 2007, CP.

[13]  Jinbo Huang.  Universal Booleanization of Constraint Models , 2008, CP.

[14]  Toby Walsh,et al.  Decompositions of Grammar Constraints , 2008, AAAI.

[15]  Toby Walsh,et al.  Circuit Complexity and Decompositions of Global Constraints , 2009, IJCAI.

[16]  Peter J. Stuckey,et al.  Lazy Clause Generation Reengineered , 2009, CP.

[17]  Adnan Darwiche,et al.  On the power of clause-learning SAT solvers as resolution engines , 2011, Artif. Intell..

[18]  G. S. Tseitin.  On the Complexity of Derivation in Propositional Calculus , 1983 .

[19]  Adnan Darwiche,et al.  A Lower Bound on the Size of Decomposable Negation Normal Form , 2010, AAAI.

[20]  Adnan Darwiche,et al.  Decomposable negation normal form , 2001, JACM.