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Journal of Logic and Computation Advance Access originally published online on August 27, 2006
Journal of Logic and Computation 2006 16(6):867-890; doi:10.1093/logcom/exl013
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© The Author, 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Logics with Common Weak Completions

Mauricio Osorio Galindo

DECFI, Universidad de las Américas, Puebla.

Juan Antonio Navarro Pérez

School of Computer Sciences, The University of Manchester, Manchester M13 9PL, UK.

José R. Arrazola Ramírez and Verónica Borja Macías

Mathematics Department, Benemérita Universidad Autónoma de Puebla, C.P. 72000, Mexico.

E-mail: mauricioj.osorio{at}udlap.mx


  Abstract

We introduce the notion of X-stable models parametrized by a given logic X. Such notion is based on a construction that we call weak completions: a set of atoms M is an X-stable model of a theory T if M is a model of T, in the sense of classical logic, and the weak completion of T (namely Formula ) can prove, in the sense given by logic X, every atom in the set M. We prove that, for normal logic programs, the result obtained by these weak completions is invariant with respect to a large family of logics. Two kinds of logics are mainly considered: paraconsistent logics and normal modal logics. For modal logics we use a translation proposed by Gelfond that identifies ¬ {square} a with ¬ a. As a consequence we prove that several semantics (recently introduced) for non-monotonic reasoning (NMR) are equivalent for normal programs. In addition, we show that such semantics can be characterized by a fixed-point operator. Also, as a side effect, we provide new results for the stable model semantics.

Keywords: Multivalued logic; paraconsistent logic; non-monotonic reasoning


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Home page
 J Logic ComputationHome page
M. O. Galindo, J. R. Arrazola Ramirez, and J. L. Carballido
Logical Weak Completions of Paraconsistent Logics
J Logic Computation, May 9, 2008; (2008) exn015v1.
[Abstract] [PDF]


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