An Axiomatic Approach to the Quantified Argument Calculus

The present article employs a model-theoretic semantics to interpret a fragment of the language of the Quantified Argument Calculus ( 𝖰𝗎𝖺𝗋𝖼 ), a recently introduced logical system whose main aim is capturing the structure of natural language sentences in a closer way than does the language of classical logic. The main contribution is an axiomatization for the set of formulas that are valid in all standard interpretations within the employed semantics.