Uniform Guarded Fragments

Jaakkola, Reijo

doi:10.1007/978-3-030-99253-8_21

Cited by 1 publication

(4 citation statements)

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“…We stress here that standard techniques for proving CIP, e.g. those based on zig-zag products [18,13,2,15], do not seem to work in our case. 2 This forces us to take a different route: we construct models explicitly by specifying types of tuples.…”

Section: :3mentioning

confidence: 88%

“…For instance, the proof can be adopted to fragments with CIP, deriving existing results (e.g. for the 2-variable GF [13] or the uniform one-dimensional GF [15]) and its failure gives hints why a certain fragment may not have CIP (e.g. in the case of full GF).…”

Section: :3mentioning

confidence: 99%

“…For instance, we believe that our technique can be adjusted, e.g. to the case of the two-variable GF from [13] as well as to the uniform one-dimensional GF from [15].…”

Section: Base Casementioning

confidence: 99%

“…For logics that are closed under negation on the level of formulas, zig-zag constructions seem to work only if the logics are one-dimensional and uniform, see[15] for more details. None of our logics are one-dimensional nor uniform.M F C S 2 0 2 2…”

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confidence: 99%

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Towards a Model Theory of Ordered Logics: Expressivity and Interpolation (Extended version)

Bednarczyk¹,

Jaakkola²

2022

Preprint

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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.

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Section: :3mentioning

confidence: 88%

Section: :3mentioning

confidence: 99%

“…For instance, we believe that our technique can be adjusted, e.g. to the case of the two-variable GF from [13] as well as to the uniform one-dimensional GF from [15].…”

Section: Base Casementioning

confidence: 99%

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confidence: 99%

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