## Analytic AGM Revision

Areces, C. and Becher, V.. Analytic AGM Revision. Technical Report CDMTCS-138, Centre for Discrete Mathematics and Theoretical Computer Science, The University of Auckland, 2000.

#### Abstract:

Since they were introduced, AGM revision and Katsuno and Mendelzon's update have been considered esentially different theory change operations serving different purposes. This work provides a new presentation of AGM revision based on the update semantic apparatus establishing in such a way a bridge between the two seemingly incomparable frameworks. We define a new operation $\bar\bullet$ as a variant of the standard update $\bullet$ that we call an analytic revision. We prove the correspondence between analytic revisions and (transitively relational) AGM revisions when a given fixed theory is considered (Theorem 4.8). Furthermore, we can characterize analytic revision functions for possibly infinite languages as those AGM revisions satisfying (K*1)-(K*8) plus two new postulates (LU-$\exists$) and (LU-$\forall$) governing the revision of different theories (Theorem 5.3). We believe these results bring new light to the issue of how revision and update functions are related. They also provide a novel way to achieve iterated theory revision.

@TECHREPORT{arec:anal00,
author = {Areces, C. and Becher, V.},
title = {Analytic AGM Revision},
institution = {Centre for Discrete Mathematics and Theoretical Computer Science,
The University of Auckland},
year = {2000},
type = {CDMTCS Research Report Series},
number = {CDMTCS-138},
abstract = {Since they were introduced, AGM revision and Katsuno and Mendelzon's
update have been considered esentially different theory change operations
serving different purposes. This work provides a new presentation
of AGM revision based on the update semantic apparatus
establishing in such a way a bridge between the two seemingly incomparable
frameworks.
We define a new operation $\bar{\bullet}$ as a variant of the standard
update $\bullet$ that we call an analytic revision. We prove the
correspondence between
analytic revisions and (transitively relational) AGM revisions when
a given fixed theory is considered (Theorem 4.8). Furthermore, we
can characterize analytic revision functions for possibly infinite
languages as those AGM revisions satisfying (K*1)-(K*8) plus two
new postulates (LU-$\exists$) and (LU-$\forall$) governing the revision
of different theories (Theorem 5.3).
We believe these results bring new light to the issue of how revision
and update functions are related. They also provide a novel way to
achieve iterated theory revision.},
owner = {areces},
timestamp = {2012.06.05}
}


Generated by bib2html.pl (written by Patrick Riley) on Sun Oct 02, 2016 17:05:49