Blocked Clauses in First-Order Logic

18 pages•Published: May 4, 2017

Benjamin Kiesl, Martin Suda, Martina Seidl, Hans Tompits and Armin Biere

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:	https://easychair.org/publications/paper/Bl2v
	https://doi.org/10.29007/c3wq

BibTeX entry

@inproceedings{LPAR-21:Blocked_Clauses_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},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/Bl2v},
  doi       = {10.29007/c3wq},
  pages     = {31-48},
  year      = {2017}}

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