Two-variable First-Order Logic with Counting in Forests

19 pages•Published: October 23, 2018

Witold Charatonik, Yegor Guskov, Ian Pratt-Hartmann and Piotr Witkowski

Abstract

We consider an extension of two-variable, first-order logic with counting quantifiers and arbitrarily many unary and binary predicates, in which one distinguished predicate is interpreted as the mother-daughter relation in an unranked forest. We show that both the finite satisfiability and the general satisfiability problems for the extended logic are decidable in NExpTime. We also show that the decision procedure for finite satisfiability can be extended to the logic where two distinguished predicates are interpreted as the mother-daughter relations in two independent forests.

Keyphrases: decision procedures, finite satisfiability, general satisfiability, logic and computational complexity, two variable logic with counting quantifiers, unranked trees/forests

In: Gilles Barthe, Geoff Sutcliffe and Margus Veanes (editors). LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 57, pages 214-232.

Links:	https://easychair.org/publications/paper/f6fB
	https://doi.org/10.29007/24fm

BibTeX entry

@inproceedings{LPAR-22:Two_variable_First_Order,
  author    = {Witold Charatonik and Yegor Guskov and Ian Pratt-Hartmann and Piotr Witkowski},
  title     = {Two-variable First-Order Logic with Counting in Forests},
  booktitle = {LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Gilles Barthe and Geoff Sutcliffe and Margus Veanes},
  series    = {EPiC Series in Computing},
  volume    = {57},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/f6fB},
  doi       = {10.29007/24fm},
  pages     = {214-232},
  year      = {2018}}

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