Duality between merging operators and social contraction operators

Authors:
José Luis Chacón;Ramón Pino Pérez
Affiliations:
Departamento de Matemáticas Facultad de Ciencias, Universidad de Los Andes, Mérida, Venezuela;Departamento de Matemáticas Facultad de Ciencias, Universidad de Los Andes, Mérida, Venezuela
Venue:
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Year:
2012

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Abstract

In the AGM (Alchourrón-Gärdenfors-Makinson) framework there exists a duality between revision operators and contraction operators. This duality is given by the Levi identity and the Harper identity. The former allows to define a revision operator starting from a contraction operator. The latter allows to define a contraction operator starting from a revision operator. In this work we show that this duality can be extended to a duality between merging operators and social contraction operators through some identities in the style of the Levi and Harper identities.