MoL-2020-18: Acosta, Ignacio Bellas (2020) Studies in the Extension of Standard Modal Logic with an Infinite Modality. [Report]
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Abstract
We consider the modal logic ML^∞, the extension of standard modal logic where the modality ♦^∞ is added to the signature. Interpreted using Kripke semantics, the ♦^∞ modality captures the distinction between finite and infinite. We first provide a collection of results on the model theoretic aspects of this logic. Introducing an alternative definition of bisimulation, we establish a collection of invariance results as well as a characterization of ML^∞ in terms of this new notion of bisimulation. Furthermore we adapt the Hennessy-Milner property to the ML^∞ framework and characterize a collection of frames that enjoy this property.
In a second line of research we establish some positive results on the finite axiomatization of ML^∞ . We introduce the ML^∞ logics K^∞ and S5^∞ and we show that they are, respectively, sound and weakly complete with respect to the class of Kripke frames and the class of equivalent Kripke frames.
| Item Type: | Report |
|---|---|
| Report Nr: | MoL-2020-18 |
| Series Name: | Master of Logic Thesis (MoL) Series |
| Year: | 2020 |
| Subjects: | Logic Mathematics |
| Depositing User: | Dr Marco Vervoort |
| Date Deposited: | 10 Jun 2025 12:34 |
| Last Modified: | 10 Jun 2025 12:34 |
| URI: | https://eprints.illc.uva.nl/id/eprint/2365 |
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