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Towards a Semantics of Unsatisfiability Proofs with Inprocessing

20 pagesPublished: May 4, 2017

Abstract

Delete Resolution Asymmetric Tautology (DRAT) proofs have become a de facto standard to certify unsatisfiability results from SAT solvers with inprocessing. However, DRAT shows behaviors notably different from other proof systems: DRAT inferences are non- monotonic, and clauses that are not consequences of the premises can be derived. In this paper, we clarify some discrepancies on the notions of reverse unit propagation (RUP) clauses and asymmetric tautologies (AT), and furthermore develop the concept of resolution consequences. This allows us to present an intuitive explanation of RAT in terms of permissive definitions. We prove that a formula derived using RATs can be stratified into clause sets depending on which definitions they require, which give a strong invariant along RAT proofs. We furthermore study its interaction with clause deletion, characterizing DRAT derivability as satisfiability-preservation.

Keyphrases: blocked clauses, DRAT proofs, SAT solving

In: Thomas Eiter and David Sands (editors). LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 46, pages 65--84

Links:
BibTeX entry
@inproceedings{LPAR-21:Towards_Semantics_of_Unsatisfiability,
  author    = {Tobias Philipp and Adri\textbackslash{}'an Rebola-Pardo},
  title     = {Towards a Semantics of Unsatisfiability Proofs with Inprocessing},
  booktitle = {LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Thomas Eiter and David Sands},
  series    = {EPiC Series in Computing},
  volume    = {46},
  pages     = {65--84},
  year      = {2017},
  publisher = {EasyChair},
  bibsource = {EasyChair, http://www.easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/V8G},
  doi       = {10.29007/7jgq}}
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