CEU Electronic Theses and Dissertations, 2017
| Author | Pavlovic, Edi |
|---|---|
| Title | The Quantified Argument Calculus: An Inquiry into Its Logical Properties and Applications |
| Summary | The topic of this dissertation is the Quantified Argument Calculus, or Quarc, and its goal to explore its formal properties, and to investigate its application to issues in philosophy. Chapter 1 briefly introduces the motivation for the forthcoming inquiry and lays out the plan of the rest of the dissertation. Chapter 2 presents the formal system of Quarc and demonstrates the completeness of it, as well as some additional features. Chapter 3 presents the sequent-calculus representation of Quarc, the LK-Quarc. It demonstrates that Quarc and LK-Quarc are deductively equivalent, and establishes the cut elimination property and its corollaries, as well as some additional features, for a series of subsystems, and finally for the full system LK-Quarc. Chapter 4 follows up on the previous chapter by demonstrating that the Craig interpolation property holds of a system closely related to LK-Quarc, and outlines venues of further research. Chapter 5 discusses the modal expansions of Quarc and LK-Quarc, as well as their relation. Cut elimination property and its corollaries are established for a range of modal systems. Chapter 6 applies some of the lessons of previous chapters to a case study of a part of Aristotle's modal syllogistic. Quarc is shown to be an appropriate tool for study of Aristotle, and then applied to establish some indicative difficulties for the modal syllogistic. |
| Supervisor | Ben-Yami, Hanoch |
| Department | Philosophy PhD |
| Full text | https://www.etd.ceu.edu/2017/pavlovic_edi.pdf |
Visit the CEU Library.
© 2007-2021, Central European University