QUARC and Classical Logic

Abstract I show that Hanoch Ben-Yami’s so-called QUantified ARgument Calculus () can be extended to what I call $$^{+}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>+</mml:mo> </mml:mmultiscripts> </mml:math> which I show to be intertranslatable with a version of first-order logic in which unary predicates are non-empty. Given this result, I show that $$^{+}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>+</mml:mo> </mml:mmultiscripts> </mml:math> is complete, propose an axiomatization of , and discuss the resulting expressive limitation of .