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<p>I show that Hanoch Ben-Yami’s so-called QUantified ARgument Calculus (<Emphasis FontCategory="SansSerif">QUARC</Emphasis>) can be extended to what I call <Emphasis FontCategory="SansSerif">QUARC</Emphasis> <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(^{+}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>+</mo> </mmultiscripts> </math></EquationSource> </InlineEquation> 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 <Emphasis FontCategory="SansSerif">QUARC</Emphasis> <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(^{+}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>+</mo> </mmultiscripts> </math></EquationSource> </InlineEquation> is complete, propose an axiomatization of <Emphasis FontCategory="SansSerif">QUARC</Emphasis>, and discuss the resulting expressive limitation of <Emphasis FontCategory="SansSerif">QUARC</Emphasis>.</p>

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QUARC and Classical Logic

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月1日

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  • Jonas Raab

摘要

I show that Hanoch Ben-Yami’s so-called QUantified ARgument Calculus (QUARC) can be extended to what I call QUARC \(^{+}\) + 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 QUARC \(^{+}\) + is complete, propose an axiomatization of QUARC, and discuss the resulting expressive limitation of QUARC.