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  • DECIDABLE FRAGMENTS OF THE QUANTIFIED ARGUMENT CALCULUS

  • Part of
  • EDI PAVLOVIĆ, NORBERT GRATZL
  • Journal:
    The Review of Symbolic Logic / Volume 17 / Issue 3 / September 2024
    Published online by Cambridge University Press:
    29 September 2023, pp. 736-761
    Print publication:
    September 2024
    • Article
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  • This paper extends the investigations into logical properties of the quantified argument calculus (Quarc) by suggesting a series of proper subsystems which, although retaining the entire vocabulary of Quarc, restrict quantification in such a way as to make the result decidable. The proof of decidability is via a procedure that prunes the infinite branches of a derivation tree in what is a syntactic counterpart of semantic filtration. We demonstrate an application of one of these systems by showing that Aristotle’s assertoric syllogistic is embeddable within, thus also providing another method of showing its decidability.