A Resolution Calculus for Second-order Logic with Eager Unification

Alexander Leitsch; Tomer Libal

doi:10.29007/zpg2

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A Resolution Calculus for Second-order Logic with Eager Unification

1 pages•Published: August 19, 2013

Alexander Leitsch and Tomer Libal

Abstract

The efficiency of the first-order resolution calculus is impaired when lifting it to higher-order logic. The main reason for that is the semi-decidability and infinitary nature
of higher-order unification algorithms, which requires the integration of unification within the calculus and results in a non-efficient search for refutations.
We present a modification of the constrained resolution calculus (Huet'72) which uses an eager unification algorithm while retaining completeness. The
algorithm is complete with regard to bounded unification only, which for many cases, does not pose a problem in practice.

Keyphrases: Bounded unification, Decidable unification problems, Efficient second-order theorem proving, Higher-order resolution, regular expressions

In: Pascal Fontaine, Renate A. Schmidt and Stephan Schulz (editors). PAAR-2012. Third Workshop on Practical Aspects of Automated Reasoning, vol 21, pages 95--95

Links:	https://easychair.org/publications/paper/dWbr
	https://doi.org/10.29007/zpg2

BibTeX entry

@inproceedings{PAAR-2012:Resolution_Calculus_for_Second_order,
  author    = {Alexander Leitsch and Tomer Libal},
  title     = {A Resolution Calculus for Second-order Logic with Eager Unification},
  booktitle = {PAAR-2012. Third Workshop on Practical Aspects of Automated Reasoning},
  editor    = {Pascal Fontaine and Renate A. Schmidt and Stephan Schulz},
  series    = {EPiC Series in Computing},
  volume    = {21},
  pages     = {95},
  year      = {2013},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/dWbr},
  doi       = {10.29007/zpg2}}

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