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<p>I develop a modal extension of the QUantified ARgument Calculus (<Emphasis FontCategory="SansSerif">QUARC</Emphasis>)—a novel logical system introduced by Hanoch Ben-Yami. <Emphasis FontCategory="SansSerif">QUARC</Emphasis> is meant to better capture the logic of natural language. The purpose of this paper is to evaluate this claim by considering how modal <Emphasis FontCategory="SansSerif">QUARC</Emphasis> (<Emphasis FontCategory="SansSerif">M-QUARC</Emphasis>) handles the Barcan and Converse Barcan Formulas and how this correlates to surrounding debates. To do so, I develop a variable domain semantics for <Emphasis FontCategory="SansSerif">M-QUARC</Emphasis> and show that even if the usual domain conditions are imposed on models with variable domains, simple <Emphasis FontCategory="SansSerif">M-QUARC</Emphasis>-<i>analogues</i> of the Barcan and Converse Barcan Formulas are not valid.<!-- Query ID="Q1" Text="Kindly check and confirm the processed city, state and country names are correct in Affiliation." --> I introduce new conditions and show that they validate the formulas. I go on to extend the language of <Emphasis FontCategory="SansSerif">M-QUARC</Emphasis> to simulate unrestricted quantification and show that in this setting the domain conditions validate the Barcan and Converse Barcan Formulas. Based on these results, I evaluate the relationship of the formal systems <Emphasis FontCategory="SansSerif">M-QUARC</Emphasis> and standard quantified modal logic with respect to one another and to natural language. I argue that if <Emphasis FontCategory="SansSerif">M-QUARC</Emphasis> does capture the logic of natural language, then natural language is capable to express neither the Barcan and Converse Barcan Formulas nor counterexamples to them. Given that, I raise doubts that <Emphasis FontCategory="SansSerif">M-QUARC</Emphasis> captures quantification as it occurs in natural language.</p>

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Modal QUARC and Barcan

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月8日

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  • Jonas Raab

摘要

I develop a modal extension of the QUantified ARgument Calculus (QUARC)—a novel logical system introduced by Hanoch Ben-Yami. QUARC is meant to better capture the logic of natural language. The purpose of this paper is to evaluate this claim by considering how modal QUARC (M-QUARC) handles the Barcan and Converse Barcan Formulas and how this correlates to surrounding debates. To do so, I develop a variable domain semantics for M-QUARC and show that even if the usual domain conditions are imposed on models with variable domains, simple M-QUARC-analogues of the Barcan and Converse Barcan Formulas are not valid. I introduce new conditions and show that they validate the formulas. I go on to extend the language of M-QUARC to simulate unrestricted quantification and show that in this setting the domain conditions validate the Barcan and Converse Barcan Formulas. Based on these results, I evaluate the relationship of the formal systems M-QUARC and standard quantified modal logic with respect to one another and to natural language. I argue that if M-QUARC does capture the logic of natural language, then natural language is capable to express neither the Barcan and Converse Barcan Formulas nor counterexamples to them. Given that, I raise doubts that M-QUARC captures quantification as it occurs in natural language.