## 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.

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#### 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.

#### BibTeX: (download)

@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} }

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