Extending the Knowledge Compilation Map: Krom, Horn, Affine and Beyond

We extend the knowledge compilation map introduced by Darwiche and Marquis with three influential propositional fragments, the Krom CNF one (also known as the bijunctive fragment), the Hom CNF fragment and the affine fragment (also known as the biconditional fragment) as well as seven additional languages based on them, and composed respectively of Krom or Hom CNF formulas, renamable Hom CNF formulas, disjunctions of Krom CNF formulas, disjunctions of Hom CNF formulas, disjunctions of Krom or Hom CNF formulas, disjunctions of renamable Hom CNF formulas, and disjunction of fine formulas. Each fragment is evaluated w.r.t. several criteria, including the complexity of basic quaries and transformation, and its spatial efficiency is also analysed.

[1]  Lakhdar Sais,et al.  Tractable Cover Compilations , 1997, IJCAI.

[2]  Bart Selman,et al.  Knowledge compilation and theory approximation , 1996, JACM.

[3]  Lucas Bordeaux,et al.  Knowledge Compilation Properties of Tree-of-BDDs , 2007, AAAI.

[4]  Pierre Marquis,et al.  On the Use of Partially Ordered Decision Graphs in Knowledge Compilation and Quantified Boolean Formulae , 2006, AAAI.

[5]  Thomas J. Schaefer,et al.  The complexity of satisfiability problems , 1978, STOC.

[6]  E. T. S. Informática.  On 2-SAT and Renamable Horn , 2000 .

[7]  Rolf Haenni,et al.  Propositional DAGs: A New Graph-Based Language for Representing Boolean Functions , 2006, KR.

[8]  Marco Cadoli,et al.  A Survey on Knowledge Compilation , 1997, AI Commun..

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

[10]  Rina Dechter,et al.  Directional Resolution: The Davis-Putnam Procedure, Revisited , 1994, KR.

[11]  Robert Schrag,et al.  Compilation for Critically Constrained Knowledge Bases , 1996, AAAI/IAAI, Vol. 1.

[12]  Pierre Marquis,et al.  Knowledge Compilation Using Theory Prime Implicates , 1995, IJCAI.

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

[14]  Alvaro Del Val.  Tractable Databases : How to Make Propositional Unit ResolutionComplete through CompilationAlvaro , 1994 .

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

[16]  Jean-Jacques Hébrard.  A Linear Algorithm for Renaming a Set of Clauses as a Horn Set , 1994, Theor. Comput. Sci..

[17]  Bart Selman,et al.  The Comparative Linguistics of Knowledge Representation , 1995, IJCAI.