MoL-2021-01: Proof theory for fragments of the modal mu-calculus

MoL-2021-01: Zenger, Lukas (2021) Proof theory for fragments of the modal mu-calculus. [Report]

[thumbnail of MoL-2021-01.text.pdf]

Download (870kB) | Preview


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
Depositing User: Dr Marco Vervoort
Date Deposited: 13 Mar 2021 22:59
Last Modified: 13 Mar 2021 22:59

Actions (login required)

View Item View Item