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Journal of Logic and Computation Advance Access published online on August 27, 2006
Journal of Logic and Computation, 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
Received January 4, 2006

Original Papers

Logics with Common Weak Completions

Mauricio Osorio Galindo 1 *, Juan Antonio Navarro Pérez 2, José R. Arrazola Ramírez 3, and Verónica Borja Macías 3

1 DECFI, Universidad de las Américas, Puebla
2 School of Computer Sciences, The University of Manchester, Manchester M13 9PL, UK
3 Mathematics Department, Benemérita Universidad Autónoma de Puebla, C.P. 72000, Mexico

* To whom correspondence should be addressed.
Mauricio Osorio Galindo, 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 T {cup} ¬{Mtilde}) 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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M. Osorio Galindo, J. R. Arrazola Ramirez, and J. L. Carballido
Logical Weak Completions of Paraconsistent Logics
J Logic Computation, December 1, 2008; 18(6): 913 - 940.
[Abstract] [PDF]


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