Towards a Model Theory of Ordered Logics: Expressivity and Interpolation
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Beitragende
Abstract
We consider the family of guarded and unguarded ordered logics, that constitute a recently rediscovered family of decidable fragments of first-order logic (FO), in which the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. While the complexities of their satisfiability problems are now well-established, their model theory, however, is poorly understood. Our paper aims to provide some insight into it. We start by providing suitable notions of bisimulation for ordered logics. We next employ bisimulations to compare the relative expressive power of ordered logics, and to characterise our logics as bisimulation-invariant fragments of FO à la van Benthem. Afterwards, we study the Craig Interpolation Property (CIP). We refute yet another claim from the infamous work by Purdy, by showing that the fluted and forward fragments do not enjoy CIP. We complement this result by showing that the ordered fragment and the guarded ordered logics enjoy CIP. These positive results rely on novel and quite intricate model constructions, which take full advantage of the "forwardness" of our logics.
Details
Originalsprache | Englisch |
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Titel | Proceedings of the 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022) |
Redakteure/-innen | Stefan Szeider, Robert Ganian, Alexandra Silva |
Herausgeber (Verlag) | Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik |
Seiten | 15:1-15:14 |
ISBN (elektronisch) | 9783959772563 |
ISBN (Print) | 978-3-95977-256-3 |
Publikationsstatus | Veröffentlicht - 1 Aug. 2022 |
Peer-Review-Status | Ja |
Publikationsreihe
Reihe | Leibniz international proceedings in informatics : LIPIcs |
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Band | 241 |
ISSN | 1868-8969 |
Externe IDs
Scopus | 85137559426 |
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Mendeley | ac7df221-9804-3256-941f-da419af60702 |
Schlagworte
ASJC Scopus Sachgebiete
Schlagwörter
- Craig Interpolation Property, expressive power, fluted fragment, guarded fragment, model checking, model theory, ordered fragments