MoL-2021-01: Zenger, Lukas (2021) Proof theory for fragments of the modal mu-calculus. [Report]
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Abstract
In this thesis we investigate the proof theory of the fragment Σ_1^μ ∪ Π_1^μ of the modal mu-calculus. This fragment consists of formulas which have syntactic fixed point alternation depth of at most one. Σ_1^μ ∪ Π_1^μ contains the building blocks for interesting concepts such as common knowledge. Moreover, it is computationally important in view of applications in database theory. We define a circular proof system and a circular tableaux system for Σ_1^μ ∪ Π_1^μ and prove soundness and completeness. We then use these systems to establish key properties of Σ_1^μ ∪ Π_1^μ such as the finite model property and Craig interpolation. Furthermore, we define infinitary proof systems for the whole modal mu-calculus and show that they are sound and complete. The main contribution of the thesis is an axiomatization of Σ_1^μ ∪ Π_1^μ as well as novel proofs of the finite model property and Craig interpolation.
| Item Type: | Report |
|---|---|
| Report Nr: | MoL-2021-01 |
| Series Name: | Master of Logic Thesis (MoL) Series |
| Year: | 2021 |
| Subjects: | Logic Mathematics |
| Depositing User: | Dr Marco Vervoort |
| Date Deposited: | 13 Mar 2021 22:59 |
| Last Modified: | 13 Mar 2021 22:59 |
| URI: | https://eprints.illc.uva.nl/id/eprint/1780 |
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