License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2018.31
URN: urn:nbn:de:0030-drops-96987
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9698/
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Madhusudan, P. ; Mathur, Umang ; Saha, Shambwaditya ; Viswanathan, Mahesh

A Decidable Fragment of Second Order Logic With Applications to Synthesis

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LIPIcs-CSL-2018-31.pdf (0.6 MB)

Abstract

We propose a fragment of many-sorted second order logic called EQSMT and show that checking satisfiability of sentences in this fragment is decidable. EQSMT formulae have an exists^*forall^* quantifier prefix (over variables, functions and relations) making EQSMT conducive for modeling synthesis problems. Moreover, EQSMT allows reasoning using a combination of background theories provided that they have a decidable satisfiability problem for the exists^*forall^* FO-fragment (e.g., linear arithmetic). Our decision procedure reduces the satisfiability of EQSMT formulae to satisfiability queries of exists^*forall^* formulae of each individual background theory, allowing us to use existing efficient SMT solvers supporting exists^*forall^* reasoning for these theories; hence our procedure can be seen as effectively quantified SMT (EQSMT) reasoning.

BibTeX - Entry

@InProceedings{madhusudan_et_al:LIPIcs:2018:9698,
  author =	{P. Madhusudan and Umang Mathur and Shambwaditya Saha and Mahesh Viswanathan},
  title =	{{A Decidable Fragment of Second Order Logic With Applications to Synthesis}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic  (CSL 2018)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Dan Ghica and Achim Jung},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9698},
  URN =		{urn:nbn:de:0030-drops-96987},
  doi =		{10.4230/LIPIcs.CSL.2018.31},
  annote =	{Keywords: second order logic, synthesis, decidable fragment}
}

Keywords: second order logic, synthesis, decidable fragment
Collection: 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)
Issue Date: 2018
Date of publication: 29.08.2018

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