Categorisation of Clauses in Conjunctive Normal Forms: Minimally Unsatisfiable Sub-clause-sets and the Lean Kernel

  • Oliver Kullmann
  • Inês Lynce
  • João Marques-Silva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4121)


Finding out that a SAT problem instance F is unsatisfiable is not enough for applications, where good reasons are needed for explaining the inconsistency (so that for example the inconsistency may be repaired). Previous attempts of finding such good reasons focused on finding some minimally unsatisfiable sub-clause-set F’ of F, which in general suffers from the non-uniqueness of F’ (and thus it will only find some reason, albeit there might be others).

In our work, we develop a fuller approach, enabling a more fine-grained analysis of necessity and redundancy of clauses, supported by meaningful semantical and proof-theoretical characterisations. We combine known techniques for searching and enumerating minimally unsatisfiable sub-clause-sets with (full) autarky search. To illustrate our techniques, we give a detailed analysis of well-known industrial problem instances.


Model Check Problem Instance User Requirement Conjunctive Normal Form Satisfying Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Oliver Kullmann
    • 1
  • Inês Lynce
    • 2
  • João Marques-Silva
    • 3
  1. 1.Computer Science DepartmentUniversity of Wales SwanseaSwanseaUK
  2. 2.Departamento de Engenharia Informática, Instituto Superior Técnico / INESC-IDUniversidade Técnica de Lisboa 
  3. 3.School of Electronics and Computer ScienceUniversity of SouthamptonSouthamptonUK

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