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.2015.648
URN: urn:nbn:de:0030-drops-54443
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Mogavero, Fabio ; Perelli, Giuseppe

Binding Forms in First-Order Logic

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Aiming to pinpoint the reasons behind the decidability of some complex extensions of modal logic, we propose a new classification criterion for sentences of first-order logic, which is based on the kind of binding forms admitted in their expressions, i.e., on the way the arguments of a relation can be bound to a variable. In particular, we describe a hierarchy of four fragments focused on the Boolean combinations of these forms, showing that the less expressive one is already incomparable with several first-order limitations proposed in the literature, as the guarded and unary negation fragments. We also prove, via a novel model-theoretic technique, that our logic enjoys the finite-model property, Craig's interpolation, and Beth's definability. Furthermore, the associated model-checking and satisfiability problems are solvable in PTime and Sigma_3^P, respectively.

BibTeX - Entry

  author =	{Fabio Mogavero and Giuseppe Perelli},
  title =	{{Binding Forms in First-Order Logic}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{648--665},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Stephan Kreutzer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-54443},
  doi =		{10.4230/LIPIcs.CSL.2015.648},
  annote =	{Keywords: First-Order Logic, Decidable Fragments, Satisfiability, Model Checking}

Keywords: First-Order Logic, Decidable Fragments, Satisfiability, Model Checking
Collection: 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)
Issue Date: 2015
Date of publication: 07.09.2015

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