Public Defense of Edi Pavlovic on The Quantified Argument Calculus: An Inquiry into Its Logical Properties and Applications

The Department of Philosophy cordially invites you to the Public Defense of the PhD Dissertation
by
Edi Pavlovic
on
The Quantified Argument Calculus: An Inquiry into Its Logical Properties and Applications

Supervisor: Hanoch Ben-Yami
Members of the Defense Committee:
Sara Negri (University of Helsinki)
Norbert Gratzl (Ludwig Maximilians-Universität München)
Chair: Michael Griffin

ABSTRACT

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