A Deductive-Complete Constrained Superposition Calculus for Ground Flat Equational Clauses

11 pages•Published: July 5, 2015

Sophie Tourret, Mnacho Echenim and Nicolas Peltier

Abstract

We describe an algorithm that generates prime implicates of equational clause sets without variables and function symbols. The procedure is based on constrained superposition rules, where constraints are used to store literals that are asserted as additional axioms (or hypotheses) during the proof search. This approach is sound and deductive-complete, and it is more ecient than previous algorithms based on conditional paramodulation. It is also more exible in the sense that it allows one to restrict the search space by imposing additional properties that the generated
implicates should satisfy (e.g., to ensure relevance).

Keyphrases: constraints, equational logic, prime implicates

In: Stephan Schulz, Leonardo De Moura and Boris Konev (editors). PAAR-2014. 4th Workshop on Practical Aspects of Automated Reasoning, vol 31, pages 94-104.

Links:	https://easychair.org/publications/paper/4Rtc
	https://doi.org/10.29007/3cp8

BibTeX entry

@inproceedings{PAAR-2014:Deductive_Complete_Constrained_Superposition,
  author    = {Sophie Tourret and Mnacho Echenim and Nicolas Peltier},
  title     = {A Deductive-Complete Constrained Superposition Calculus for Ground Flat Equational Clauses},
  booktitle = {PAAR-2014. 4th Workshop on Practical Aspects of Automated Reasoning},
  editor    = {Stephan Schulz and Leonardo De Moura and Boris Konev},
  series    = {EPiC Series in Computing},
  volume    = {31},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/4Rtc},
  doi       = {10.29007/3cp8},
  pages     = {94-104},
  year      = {2015}}

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