BDI: A New Decidable First-order Clause Class

13 pages•Published: July 28, 2014

Manuel Lamotte-Schubert and Christoph Weidenbach

Abstract

BDI (Bounded Depth Increase) is a new decidable
first-order clause class. It strictly includes
known classes such as PVD. The arity
of function and predicate symbols as well as the
shape of atoms is not restricted in BDI. Instead
the shape of "cycles" in resolution inferences is
restricted such that the depth of generated clauses
may increase but is still finitely bound.
The BDI class is motivated by real world problems
where function terms are used to represent record structures.

We show that the hyper-resolution calculus modulo
redundancy elimination terminates on BDI clause sets.
Employing this result to the ordered resolution calculus,
we can also prove termination of ordered resolution on BDI,
yielding a more efficient decision procedure.

Keyphrases: clauses, decidability, first order, hyper resolution, ordered resolution, resolution, superposition

In: Ken Mcmillan, Aart Middeldorp, Geoff Sutcliffe and Andrei Voronkov (editors). LPAR-19. 19th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 26, pages 62-74.

Links:	https://easychair.org/publications/paper/Ccc
	https://doi.org/10.29007/8m7f

BibTeX entry

@inproceedings{LPAR-19:BDI_New_Decidable_First,
  author    = {Manuel Lamotte-Schubert and Christoph Weidenbach},
  title     = {BDI: A New Decidable First-order Clause Class},
  booktitle = {LPAR-19. 19th International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Ken Mcmillan and Aart Middeldorp and Geoff Sutcliffe and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {26},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/Ccc},
  doi       = {10.29007/8m7f},
  pages     = {62-74},
  year      = {2014}}

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