Tableaux between proving, projection and compilation

Generalized methods for automated theorem proving can be used to compute formula transformations such as projection elimination and knowledge compilation. We present a framework based on clausal tableaux suited for such tasks. These tableaux are characterized independently of particular construction methods, but important features of empirically successful methods are taken into account, especially dependency directed backjumping and branch local operation. As an instance of that framework an adaption of DPLL is described. We show that knowledge compilation methods can be essentially improved by weaving projection elimination partially into the compilation phase.

[1]  Bernhard Beckert TABLEAUX 2005 Position Papers and Tutorial Descriptions , 2005 .

[2]  Kenneth L. McMillan,et al.  Applying SAT Methods in Unbounded Symbolic Model Checking , 2002, CAV.

[3]  Roberto J. Bayardo,et al.  Counting Models Using Connected Components , 2000, AAAI/IAAI.

[4]  Masaki Ogino,et al.  Getting closer: How Simulation and Humanoid League can benefit from each other , 2005, AMiRE.

[5]  Lutz Priese,et al.  Some Examples of Semi-rational and Non-semi-rational DAG Languages , 2006 .

[6]  Philipp Schaer,et al.  State-of-the-Art: Interaktion in Erweiterten Realitäten , 2007 .

[7]  Melanie Volkamer,et al.  Security Requirements for Non-political Internet Voting , 2006, Electronic Voting.

[8]  Neil V. Murray,et al.  Tableaux, Path Dissolution, and Decomposable Negation Normal Form for Knowledge Compilation , 2003, TABLEAUX.

[9]  Andreas Winter,et al.  Metamodel-driven Service Interoperability , 2005 .

[10]  Steffen Staab,et al.  TwoUse: Integrating UML models and OWL ontologies , 2007 .

[11]  Dov M. Gabbay,et al.  Quantifier Elimination in Second-Order Predicate Logic , 1992, KR.

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

[13]  Kenneth L. McMillan,et al.  Applications of Craig Interpolants in Model Checking , 2005, TACAS.

[14]  Cesare Tinelli,et al.  Solving SAT and SAT Modulo Theories: From an abstract Davis--Putnam--Logemann--Loveland procedure to DPLL(T) , 2006, JACM.

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

[16]  Adnan Darwiche,et al.  DPLL with a Trace: From SAT to Knowledge Compilation , 2005, IJCAI.

[17]  Adnan Darwiche,et al.  New Advances in Compiling CNF into Decomposable Negation Normal Form , 2004, ECAI.

[18]  Andreas von Hessling Semantic User Profiles and their Applications in a Mobile Environment , 2004 .

[19]  François Bry,et al.  Positive Unit Hyperresolution Tableaux and Their Application to Minimal Model Generation , 2004, Journal of Automated Reasoning.

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

[21]  Jürg Kohlas,et al.  Propositional Information Systems , 1999, J. Log. Comput..

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

[23]  Achim Rettinger,et al.  Intelligent exploration for genetic algorithms: using self-organizing maps in evolutionary computation , 2008, GECCO '05.

[24]  Benno Stein,et al.  Proceedings of the Second International Workshop on Text-Based Information Retrieval , 2005 .

[25]  Roberto J. Bayardo,et al.  Using CSP Look-Back Techniques to Solve Real-World SAT Instances , 1997, AAAI/IAAI.

[26]  Joachim Baumeister,et al.  Knowledge Engineering and Software Engineering , 2005 .

[27]  Sharad Malik,et al.  The Quest for Efficient Boolean Satisfiability Solvers , 2002, CAV.

[28]  Cesare Tinelli,et al.  Abstract DPLL and Abstract DPLL Modulo Theories , 2005, LPAR.

[29]  Jürgen Ebert,et al.  A first proposal for an overall structure of an enhanced reality framework , 2007 .

[30]  E. Hoogland Definability and Interpolation: Model-theoretic investigations , 2001 .

[31]  Patrick E. O'Neil,et al.  System Description , 2005 .

[32]  Bart Selman,et al.  Forming Concepts for Fast Inference , 1992, AAAI.

[33]  Oliver Obst,et al.  HTN Planning for Flexible Coordination Of Multiagent Team Behavior , 2005 .

[34]  Toshiaki Arai,et al.  Hybrid State Machines with Timed Synchronization for Multi-Robot System Specification , 2005, 2005 portuguese conference on artificial intelligence.

[35]  Christoph Wernhard,et al.  Semantic Knowledge Partitioning , 2004, JELIA.

[36]  Reiner Hähnle,et al.  Normal Forms for Knowledge Compilation , 2005, ISMIS.

[37]  Anastasia Meletiadou,et al.  Begriffsbestimmung und erwartete Trends im IT-Risk-Management , 2007 .

[38]  Steffen Staab,et al.  Adding Formal Semantics to MPEG-7: Designing a Well-Founded Multimedia Ontology for the Web , 2007 .

[39]  Jürgen Ebert,et al.  Web Engineering does profit from a Functional Approach , 2005 .

[40]  Francesco M. Donini,et al.  Is Intractability of Non-Monotonic Reasoning a Real Drawback? , 1994, AAAI.

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