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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