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Documents authored by Avron, Arnon

Document
DOI: 10.4230/LIPIcs.CSL.2018.8
Safety, Absoluteness, and Computability

Authors: Arnon Avron, Shahar Lev, and Nissan Levi

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
The semantic notion of dependent safety is a common generalization of the notion of absoluteness used in set theory and the notion of domain independence used in database theory for characterizing safe queries. This notion has been used in previous works to provide a unified theory of constructions and operations as they are used in different branches of mathematics and computer science, including set theory, computability theory, and database theory. In this paper we provide a complete syntactic characterization of general first-order dependent safety. We also show that this syntactic safety relation can be used for characterizing the set of strictly decidable relations on the natural numbers, as well as for characterizing rudimentary set theory and absoluteness of formulas within it.
Cite as

Arnon Avron, Shahar Lev, and Nissan Levi. Safety, Absoluteness, and Computability. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{avron_et_al:LIPIcs.CSL.2018.8,
  author =	{Avron, Arnon and Lev, Shahar and Levi, Nissan},
  title =	{{Safety, Absoluteness, and Computability}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.8},
  URN =		{urn:nbn:de:0030-drops-96754},
  doi =		{10.4230/LIPIcs.CSL.2018.8},
  annote =	{Keywords: Dependent Safety, Computability, Absoluteness, Decidability, Domain Independence}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2016.7
Minimal Paradefinite Logics for Reasoning with Incompleteness and Inconsistency

Authors: Ofer Arieli and Arnon Avron

Published in: LIPIcs, Volume 52, 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)

Abstract
Paradefinite (`beyond the definite') logics are logics that can be used for handling contradictory or partial information. As such, paradefinite logics should be both paraconsistent and paracomplete. In this paper we consider the simplest semantic framework for defining paradefinite logics, consisting of four-valued matrices, and study the better accepted logics that are induced by these matrices.
Cite as

Ofer Arieli and Arnon Avron. Minimal Paradefinite Logics for Reasoning with Incompleteness and Inconsistency. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{arieli_et_al:LIPIcs.FSCD.2016.7,
  author =	{Arieli, Ofer and Avron, Arnon},
  title =	{{Minimal Paradefinite Logics for Reasoning with Incompleteness and Inconsistency}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-010-1},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{52},
  editor =	{Kesner, Delia and Pientka, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.7},
  URN =		{urn:nbn:de:0030-drops-59731},
  doi =		{10.4230/LIPIcs.FSCD.2016.7},
  annote =	{Keywords: Paraconsistecy, Paracompleteness, 4-valued logics}
}
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