Decidable Fragments of the Quantified Argument Calculus

Review of Symbolic Logic:1-26 (forthcoming)
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Abstract

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.

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Edi Pavlović
Ludwig Maximilians Universität, München

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References found in this work

On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
A note on the entscheidungsproblem.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (1):40-41.
``A Note on the Entcheidunsproblem".Alonzo Church - 1936 - Journal of Symbolic Logic 1 (1):40-41.

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