Existential fixed-point logic, universal quantifiers, and topoi

Authors:
Andreas Blass
Affiliations:
Mathematics Department, University of Michigan, Ann Arbor, MI
Venue:
Fields of logic and computation
Year:
2010

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Abstract

When one views (multi-sorted) existential fixed-point logic (EFPL) as a database query language, it is natural to extend it by allowing universal quantification over certain sorts. These would be the sorts for which one has the "closed-world" information that all entities of that sort in the real world are represented in the database. We investigate the circumstances under which this extension of EFPL retains various pleasant properties. We pay particular attention to the pleasant property of preservation by the inverse-image parts of geometric morphisms of topoi, because, as we show, this preservation property implies many of the other pleasant properties of EFPL.