Analytic AGM Revision

C. Areces and V. Becher. 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

@TechReport{Areces2000a,
  author =       "C. Areces and V. Becher",
  institution =  "Centre for Discrete Mathematics and Theoretical
                 Computer Science, The University of Auckland",
  title =        "Analytic {AGM} Revision",
  year =         "2000",
  number =       "CDMTCS-138",
  series =       "CDMTCS Research Report Series",
  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",
}