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.2016.34
URN: urn:nbn:de:0030-drops-65746
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6574/
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Bana, Gergei ; Okada, Mitsuhiro

Semantics for "Enough-Certainty" and Fitting's Embedding of Classical Logic in S4

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Abstract

In this work we look at how Fitting's embedding of first-order classical logic into first-order S4 can help in reasoning when we are interested in satisfaction "in most cases", when first-order properties are allowed to fail in cases that are considered insignificant. We extend classical semantics by combining a Kripke-style model construction of "significant" events as possible worlds with the forcing-Fitting-style semantics construction by embedding classical logic into S4. We provide various examples. Our main running example is an application to symbolic security protocol verification with complexity-theoretic guarantees. In particular, we show how Fitting's embedding emerges entirely naturally when verifying trace properties in computer security.

BibTeX - Entry

@InProceedings{bana_et_al:LIPIcs:2016:6574,
  author =	{Gergei Bana and Mitsuhiro Okada},
  title =	{{Semantics for "Enough-Certainty" and Fitting's Embedding of Classical Logic in S4}},
  booktitle =	{25th EACSL Annual Conference on Computer Science Logic (CSL 2016)},
  pages =	{34:1--34:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-022-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{62},
  editor =	{Jean-Marc Talbot and Laurent Regnier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6574},
  URN =		{urn:nbn:de:0030-drops-65746},
  doi =		{10.4230/LIPIcs.CSL.2016.34},
  annote =	{Keywords: first-order logic, possible-world semantics, Fitting embedding, asymptotic probabilities, verification of complexity-theoretic properties}
}

Keywords: first-order logic, possible-world semantics, Fitting embedding, asymptotic probabilities, verification of complexity-theoretic properties
Collection: 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)
Issue Date: 2016
Date of publication: 29.08.2016

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