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Blocked Clauses in First-Order Logic

18 pagesPublished: May 4, 2017

Abstract

Blocked clauses provide the basis for powerful reasoning techniques used in SAT, QBF, and DQBF solving. Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper, we lift the notion of blocked clauses to first-order logic. We introduce two types of blocked clauses, one for first-order logic with equality and the other for first-order logic without equality, and prove their redundancy. In addition, we give a polynomial algorithm for checking whether a clause is blocked. Based on our new notions of blocking, we implemented a novel first-order preprocessing tool. Our experiments showed that many first-order problems in the TPTP library contain a large number of blocked clauses whose elimination can improve the performance of modern theorem provers, especially on satisfiable problem instances.

Keyphrases: automated reasoning, automated theorem proving, blocked clauses, clause elimination, first-order logic, Preprocessing, SAT

In: Thomas Eiter and David Sands (editors). LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 46, pages 31--48

Links:
BibTeX entry
@inproceedings{LPAR-21:Blocked_Clauses_in_First_Order,
  author    = {Benjamin Kiesl and Martin Suda and Martina Seidl and Hans Tompits and Armin Biere},
  title     = {Blocked Clauses in First-Order Logic},
  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     = {31--48},
  year      = {2017},
  publisher = {EasyChair},
  bibsource = {EasyChair, http://www.easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/Bl2v},
  doi       = {10.29007/c3wq}}
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